The answers are sin angle R = ST/RT and sin angle L = 3(ST)/3(RT) Fοr the given questiοn trigοnοmetry.
Thus option A & B are correct.
What is trigοnοmetric ratiοs?Trigοnοmetric ratiοs are mathematical relatiοnships between the sides and angles οf a right triangle. The three main trigοnοmetric ratiοs are sine, cοsine, and tangent, abbreviated as sin, cοs, and tan.
The sine οf an angle is the ratiο οf the length οf the side οppοsite the angle tο the length οf the hypοtenuse. The cοsine οf an angle is the ratiο οf the length οf the adjacent side tο the length οf the hypοtenuse. The tangent οf an angle is the ratiο οf the length οf the οppοsite side tο the length οf the adjacent side. These ratiοs are useful in sοlving prοblems invοlving right triangles and have many applicatiοns in fields such as physics, engineering, and navigatiοn.
We knοw that when a triangle is dilated by a scale factοr οf k, all cοrrespοnding sides are multiplied by k, and all cοrrespοnding angles remain cοngruent.
Using this fact, we can determine the relatiοnships between the trigοnοmetric ratiοs οf the twο triangles:
A. Sin angle R = ST/RT is true fοr bοth triangles, as the sine οf an angle is defined as the ratiο οf the οppοsite side tο the hypοtenuse, which dοes nοt change when dilated.
B. Sin angle L = 3(ST)/3(RT)simplifies tο Sin angle L = ST/RT, which is true fοr bοth triangles (as shοwn in part A).
C. Sin angle R = 3(MN)/3(LM) simplifies tο sin angle R = MN/LM, which is nοt necessarily true. This is because the cοrrespοnding sides οf the triangles are nοt prοpοrtiοnal tο each οther.
D. Sin angle L = MN/NL is nοt necessarily true fοr the same reasοn as in part C.
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A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 17 12 27 44
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
Therefore , the solution of the given problem of unitary method comes out to be the quantitative data being displayed, is best displayed using a bar graph.
What is a unitary method?The task may be completed using this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, you may have another opportunity to interact with the item. Otherwise, all significant factors that affect how algorithmic factor proof behaves will be gone.
Here,
The right graph is option (a),
a bar graph with the heading "Favorite Topping" and the axes "Topping" and "Number of Customers" written on them. T
he labels for the bars should read "Chocolate Chips" with a value of 44, "Hot Fudge" with a value of 27, "Nuts" with a value of 12, and "Sprinkles" with a value of 17.
This categorical data, where each topping is a distinct category and the number of customers is the quantitative data being displayed, is best displayed using a bar graph.
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Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 and deposits $66 per month into his account.
Answer: muhammad will $99 in one month and connor will have $8
Step-by-step explanation:
$158-$59=$99
$74-$66=$8
A farmer sells 7.1 kilograms of apples and pears at the farmer's market. 4
5
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? What is it in fraction form it has to converted by a decimal.
The farmer sold approximately 3.905 kilograms of pears at the farmer's market. In fraction form, this is 781/200 kilograms.
PLEASE help
Allen mixes 1 cup of water that is 150°F and 1 cup of cold chicken broth that is 50°F. The end temperature of the mixture would be about___________
. Chris combines 2 cups of soup that is 50°F with 1 cup of water that is 150°F. The end temperature of the mixture would be ______
Answer:
1) 100 degrees F
2) 50 degrees F
Step-by-step explanation:
its just simple subtraction
According to the records of an insurance company, the payouts on insurance cases in February were $12,400. In March, the payouts increased by 8.5% and then dropped by 5% in April. Find the amount of the payouts in April.
Let the amount of payouts in March be M.
From the problem, we know that the payouts in March increased by 8.5%, which means:
M = 12,400 + 0.085(12,400)
M = 12,400 + 1,054
M = 13,454
Next, we know that the payouts in April dropped by 5%, which means:
A = M - 0.05M
A = 0.95M
A = 0.95(13,454)
A = 12,781.3
Therefore, the amount of the payouts in April was $12,781.3.
Which of the following is the graph of y = negative (x minus 2) cubed minus 5?
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4.
On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3.
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4.
On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Answer:
3rd
steps
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4
chatgpt
height of a ball thrown into the air can be modeled by a cubic function
please help i have until saturday
The height of the square pyramid with the given slant height base base length is found as: 91.17 in.
Explain about the square pyramid?A square pyramid is really a pyramid with only a square base. A pentahedron, that is. With a base and three triangle sides, a pyramid is a 3D shape.
A square base is what a pyramid with a square base is built upon. A great illustration of a square-based pyramid is the Egyptian pyramid complex.
A right square pyramid with side length a with height h has lateral edge length e as well as slant height s.
Given data:
Slant height s = 91.8 in.
Height H = ?
Base length a = 21.4 in.
Slant height s formula is:
s² = H² + 1/4 a²
H² = s² - 1/4 a²
H² = 91.8² - 1/4 *(21.4)²
H = √8312.75
H = 91.17 in.
Thus, the height of the square pyramid with the given slant height and base length is found as: 91.17 in.
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The height of the square pyramid with the given slant height base base length is about 91.2 in. to one decimal place
What is a square pyramid?A square pyramid is a polyhedron that has a square base and four lateral faces that meet at a point above the base (e.g. the apex)
The given parameters to solve the question are given as follows
Slant height s = 91.8 in.
Height H = ?
Base length a = 21.4 in.
Slant height s formula is: s² = H² + 1/4 a²
H² = s² - 1/4 a²
By substitution into the formula we have
H² = 91.8² - 1/4 *(21.4)²
H = √8312.75
H = 91.17 in.
Thus, the height of the square pyramid with the given slant height and base length is found as: 91.2 in.
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what is the value of x?
Answer:3
Step-by-step explanation: becuase the big one was 40 and the smaller one was four, so it is probably 3
please help!! If I roll a dice, flip a coin, and then pull a card out of the deck; what are the odds that I roll an even number, get tail, AND I pull a red card out of the deck?
Therefore, the odds of rolling an even number, getting a tail, and pulling a red card are 1 in 8 or 1/8.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves calculating the likelihood or chance of an event occurring based on the available information and assumptions. Probability is commonly used in many fields, including science, engineering, finance, and statistics. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
Here,
The probability of rolling an even number on a fair six-sided dice is 3/6 or 1/2. The probability of flipping a tail on a fair coin is 1/2. The probability of pulling a red card out of a standard deck of 52 playing cards is 26/52 or 1/2 (assuming the deck is well shuffled).
To find the probability of all three events occurring together, we multiply the probabilities of each individual event:
=P(rolling an even number) x P(getting tail) x P(pulling a red card)
= 1/2 x 1/2 x 1/2
= 1/8
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Widmer Company had gross wages of $350,000 during the week ended June 17. The amount of wages subject to social security tax was $350,000, while the amount of wages subject to federal and state unemployment taxes was $52,500. Tax rates are as follows:
Line Item Description Percentage
Social security 6. 0%
Medicare 1. 5%
State unemployment 5. 4%
Federal unemployment 0. 8%
The total amount withheld from employee wages for federal taxes was $70,000
The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000, Social security tax =$21,000 , Medicare tax = $5,250 , State unemployment tax =$2,835 , Federal unemployment tax = $420 and Total taxes = $29,505 .
To calculate the amount of taxes that Widmer Company owes for the week ended June 17, we need to calculate each tax separately and then add them together.
First, let's calculate the social security tax. The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000. So:
Social security tax = 6.0% x $350,000 = $21,000
Next, let's calculate the Medicare tax. The tax rate for Medicare is 1.5%, and the amount of wages subject to this tax is also $350,000. So:
Medicare tax = 1.5% x $350,000 = $5,250
Now let's calculate the state unemployment tax. The tax rate for state unemployment is 5.4%, and the amount of wages subject to this tax is $52,500. So:
State unemployment tax = 5.4% x $52,500 = $2,835
Finally, let's calculate the federal unemployment tax. The tax rate for federal unemployment is 0.8%, and the amount of wages subject to this tax is also $52,500. So:
Federal unemployment tax = 0.8% x $52,500 = $420
Now let's add up all of the taxes:
Total taxes = Social security tax + Medicare tax + State unemployment tax + Federal unemployment tax
Total taxes = $21,000 + $5,250 + $2,835 + $420
Total taxes = $29,505
This means that Widmer Company owes $29,505 in taxes for the week ended June 17.
Additionally, we are told that the total amount withheld from employee wages for federal taxes was $70,000. This means that the company must remit this amount to the federal government as federal income tax on behalf of its employees. The $70,000 does not affect the company's own tax liability, but rather is an amount owed to the federal government by the employees themselves.
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ZC and ZD are vertical angles with mzC = -3x + 58 and m/D = x - 2.
what is the value of m/D
enter your answer in the box. enter only the num erical value ( do not enter units)
The measure of [tex]\angle D[/tex] is 13.
What are vertical angles?Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.
given:
[tex]m\angle C=-3x+58[/tex] and [tex]m\angle D=x-2[/tex]
As, [tex]\angle C[/tex] and [tex]\angle D[/tex] are vertical angles
so,
[tex]m\angle C= m\angle D[/tex]
[tex]-3x+58 = x-2[/tex]
[tex]-3x -x = -2-58[/tex]
[tex]-4x = -60[/tex]
[tex]x= 15[/tex]
So, [tex]m\angle D= x-2= 15-2 = 13[/tex]
Hence, the value of [tex]m\angle D[/tex] is 13.
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Find the conditional Probability
P ( Male and Independent voter l Independent voter )
Group of answer choices
68.4 %
45.2 %
31.6 %
40.6 %
The value of the conditional probability from the Venn Diagram is (a) 68.4 %
Calculating the value of the conditional probabilityGiven that we have the Venn Diagram
From the Venn Diagram, we have the following readings
Male and Independent voters = 13
Independent voters = 19
Using the above values, we have the following equation
P(Male | Independent voter) = 13/19
Evaluate
P(Male | Independent voter) = 68.4 %
Hence, the conditional probability is 68.4 %
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can yall pls help me with this I will be so happy if you do!
Answer:
Step-by-step explanation:
I changed it v to X because it's more convenient for me, but please write "v" so don't forget!
the chance of rain on a given day in seattle is 70%. if it rains, the chance that a food truck will incur a loss on that day is 80%. if it does not rain, then the chance of loss is 10%. on a randomly chosen day if the food truck has not incurred a loss, what is the probability that it had not rained that day?
The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.
The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.
The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.
To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.
The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%
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at an airport, 77% of recent flights have arrived on time. a sample of 11 flights is studied for the binomial experiment. find the probability that no more than 4 of them were on time. group of answer choices 0.0046
The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.19036 or 0.0046 (rounded to four decimal places).
The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.0046.
Binomial probability distribution is defined as a distribution where only two outcomes are possible - success or failure - and each trial is independent of other trials.
A binomial experiment is one that meets the following four conditions:
1. Each trial has only two outcomes (success or failure).
2. The probability of success remains constant across all trials.
3. The trials are independent of each other.
4. The experiment involves a fixed number of trials.
In this case, the probability of success is 77% or 0.77 since that is the probability that a recent flight arrives on time.
The probability of failure is 1 - 0.77 = 0.23 since it's the probability that a recent flight does not arrive on time.
Let's use these values to solve the problem.
The probability of no more than 4 flights arriving on time in a sample of 11 flights where 77% of recent flights arrived on time is given by the cumulative probability of x ≤ 4, which is equal to:
P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)
where:P(x = 0) = (11 C 0) (0.77)0 (0.23)11 = 0.0001267
P(x = 1) = (11 C 1) (0.77)1 (0.23)10 = 0.0017314
P(x = 2) = (11 C 2) (0.77)2 (0.23)9 = 0.0115321
P(x = 3) = (11 C 3) (0.77)3 (0.23)8 = 0.0474373
P(x = 4) = (11 C 4) (0.77)4 (0.23)7 = 0.1295333
Now we can add these values to find the probability of no more than 4 flights arriving on time in a sample of 11 flights:
P(x ≤ 4) = 0.0001267 + 0.0017314 + 0.0115321 + 0.0474373 + 0.1295333= 0.19036
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The resident population, p, in a New York town has been decreasing for years. The table below shows the population of the town t years after 2010.
Answer:
where is the table without the table how can I give the answer
The first and third term of a geometric progression (GP) are 2 and 2/9 respectively, find the common ratio and the fifth term
The common ratio is 1/3 and the fifth term of a geometric progression (GP) is 2/81 if the first and third terms of the GP are 2 and 2/9, respectively.
Let's call the common ratio of the GP "r".
We know that the first term of the GP is 2, so:
a₁ = 2
We also know that the third term of the GP is 2/9, so:
a₃ = 2/9
We can write the following using the nth term of a GP formula:
a₃ = a₁ * r²
Substituting the values we know, we get:
2/9 = 2 * r²
Dividing both sides by 2, we get:
1/9 = r²
Taking the square root of both sides (and remembering that r must be positive since it's a common ratio), we get:
r = 1/3
Now we can find the fifth term of the GP using the formula:
a₅ = a₁ * r⁴
Substituting the values we know, we get:
a₅ = 2 * (1/3)⁴
a₅ = 2 * (1/81)
a₅ = 2/81
Therefore, the common ratio is 1/3 and the fifth term of the GP is 2/81.
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The ratio of apples to bananas in a bowl of fruit is 2 to
3. If there are 12 apples in the bowl, then how many
bananas are there?
Answer:18
Step-by-step explanation:
2x=12
3x=?
2x/2=12/2= x=6
3(6)=18
Which side lengths form a right triangle?
A) 3, [tex]\sqrt{9}[/tex], [tex]\sqrt{18}[/tex]
B) 3, 4, 5
C) 7, 7, [tex]\sqrt{98}[/tex]
Only option B) 3, 4, and 5 forms a right triangle.
What is the Pythagorean theorem?
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.
So, to check which set of side lengths form a right triangle, we need to see if they satisfy this condition.
A) 3, √9,√18:
√9 is equal to 3, so we have the side lengths 3, 3√2.
Using the Pythagorean theorem:
(3)² + (3√2)² = 9 + 18 = 27
However, (√18)² is also equal to 18, so the set of side lengths can also be written as 3, 3√2, √18.
Using the Pythagorean theorem again:
(3)² + (3√2)² = 9 + 18 = 27
and (3)² + (√18)² = 9 + 18 = 27
So, we have two sides that can form a right triangle, but not all three.
B) 3, 4, 5:
Using the Pythagorean theorem:
(3)² + (4)² = 9 + 16 = 25
Since 5² is also equal to 25, these side lengths form a right triangle.
C) 7, 7, √98:
√98 can be simplified as 7√2. So, we have the side lengths 7, 7, 7√2.
Using the Pythagorean theorem:
(7)² + (7)² = 98
and (7)² + (7√2)² = 343 + 98 = 441
So, we don't have a right triangle in this case.
Therefore, only option B) 3, 4, and 5 forms a right triangle.
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HELPPPPPP! PLEASE- ANSWER QUICKLY.
(Subject: Highschool Algebra)
The solution to the simultaneous equation represented on the graph is:
B: x = 2 and x = 4
How to find the solution of the equation graph?We are given the equations as:
f(x) = -12x + 26
g(x) = -(-¹/₅)^(-x + 2) + 3
The solution to these two simultaneous equations will be the coordinates of the points on the graph where they both intersect.
We see that the coordinates of the points of intersection of the graph is at the coordinates:
(2, 2) and (4, -22)
Thus, the solution is at x = 2 and x = 4
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Line s has an equation of y–2= – 4(x+1). Line t includes the point ( – 1,6) and is parallel to line s. What is the equation of line t?
The equation of line t, which is parallel to line s and passes through point (–1,6), is y = -4x + 2.
We can start by finding the slope of line s, since line t is parallel to line s it will have the same slope.
y – 2 = –4(x + 1) [Given equation of line s in point-slope form]
y – 2 = –4x – 4 [Distribute -4 on the right side]
y = –4x – 2 [Add 2 to both sides to get the equation in slope-intercept form y = mx + b where m = slope and b = y-intercept]
So the slope of line s is -4.
Since line t is parallel to line s, it will also have a slope of -4. Now we can use the point-slope form of the equation of a line to find the equation of line t:
y - y1 = m(x - x1) [Point-slope form of the equation of a line]
We know that line t includes the point (–1,6), so x1 = –1 and y1 = 6. Also, the slope of line t is m = -4. Substituting these values in the point-slope form, we get:
y - 6 = -4(x - (-1))
y - 6 = -4(x + 1)
y - 6 = -4x - 4
y = -4x + 2
Therefore, the equation of line t is y = -4x + 2.
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Some students were asked about their daily exercise.
12 more students answered Yes than answered No.
Complete the frequency tree.
___________________________
One of the 35 students who answered Yes is chosen at random .
What is the probability that they exercise for at least 1 hour?
So the minimum probability that a Yes respondent exercises for at least 1 hour is 6/(x+6), where x is the number of students who answered No.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields such as mathematics, statistics, science, economics, and finance to model and analyze uncertain situations.
Here,
Let the number of students who answered No be x. Then the number of students who answered Yes is x+12. The total number of students is then x + (x+12) = 2x + 12.
Suppose y of the students who answered Yes exercise for at least 1 hour. Then the probability that a Yes respondent exercises for at least 1 hour is y/(x+12).
Since we don't have the full frequency tree, we can't determine y or x directly. However, we do know that the total number of students who exercise for at least 1 hour is greater than or equal to 12 (since there are 12 more Yes respondents than No respondents). Therefore, the probability that a Yes respondent exercises for at least 1 hour is y/(x+12) is at least 12/(2x+12) = 6/(x+6).
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A bycicle wheel whose radius is 30 cm covered distance in 70 revolutions how many km was the distance
Answer:
0.13188 km
Step-by-step explanation:
The distance covered by the bicycle wheel can be calculated using the formula:
distance = circumference x number of revolutions
The circumference of the wheel can be calculated using the formula:
circumference = 2 x pi x radius
where pi is approximately equal to 3.14.
Substituting the given values:
circumference = 2 x 3.14 x 30 cm
circumference = 188.4 cm
Now, we can calculate the distance covered by the wheel:
distance = circumference x number of revolutions
distance = 188.4 cm x 70
distance = 13188 cm
To convert this distance from centimeters to kilometers, we need to divide by 100,000 (since there are 100,000 centimeters in a kilometer):
distance = 13188 cm ÷ 100,000
distance = 0.13188 km
Therefore, the distance covered by the bicycle wheel is approximately 0.13188 km.
What is DE (Please answer with work and an explanation)
Answer:
(added to verbs and their derivatives) denoting removal or reversal.
Step-by-step explanation:
In the pentagon shown below, the ratio of the size of
angle DEA to the size of angle CDE is 5 2. The ratio
of the size of angle EAB to the size of angle ABC is
4:3.
What is the size of angle EAB?
Give your answer in degrees.
D
50°
A
106°
B
C
Not drawn accurately
The size of angle EAB is approximately 70.76 degrees.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Let's start with the ratio of the size of angle DEA to the size of angle CDE. We can express this ratio as:
angle DEA : angle CDE = 5 : 2
We know that the sum of the angles in a triangle is 180 degrees, so we can use this fact to express angle DEA and angle CDE in terms of angle ABD:
angle DEA + angle CDE + angle ABD = 180
Substituting the ratio given above, we get:
5x + 2x + angle ABD = 180
Simplifying, we get:
7x + angle ABD = 180
Next, let's consider the ratio of the size of angle EAB to the size of angle ABC, which is given as 4:3. We can express this ratio as:
angle EAB : angle ABC = 4 : 3
We know that angle EAB and angle ABC are adjacent angles, so their sum is equal to angle ABD:
angle EAB + angle ABC = angle ABD
Substituting the ratio given above, we get:
4y + 3y = angle ABD
Simplifying, we get:
7y = angle ABD
Now we have two equations:
7x + angle ABD = 180
7y = angle ABD
We can substitute the second equation into the first to get an equation in terms of y:
7x + 7y = 180
Simplifying, we get:
x + y = 25.71
Now we can use the ratio of angle EAB to angle ABC to find y:
angle EAB : angle ABC = 4 : 3
4y : 3y = 4 : 3
Simplifying, we get:
4y = 3(106 - angle EAB)
Expanding, we get:
4y = 318 - 3angle EAB
Substituting the equation we found for y above, we get:
4(25.71 - x) = 318 - 3angle EAB
Simplifying, we get:
angle EAB = 70.76
Therefore, the size of angle EAB is approximately 70.76 degrees.
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Can someone help? Also need to show work
The measure of w in the adjacent angle is 30 degrees.
How to find the adjacent angles?The two angles are said to be adjacent angles when they share the common vertex and side. In other words, adjace3nt angles have common side and common vertex.
Therefore, let's find the measure of angle w as follows:
Hence, the sum of angle w and angle 50 degrees is equals to 80 degrees.
Therefore,
50 + w = 80
subtract 50 from both sides of the equation
50 - 50 + w = 80 - 50
w = 30 degrees
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due to the long distance and limited capacity, nm must place the order 6 months in advance. a detailed analysis of past data shows that if forecasting 6 month in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 60. what is the optimal number of bags to purchase?
The optimal number of bags to purchase is 174 bags.
To determine the optimal number of bags to purchase, we need to consider the trade-off between the cost of holding excess inventory and the cost of not having enough inventory to meet demand.
Let's assume that the cost of holding one bag of inventory for six months is $2.00, and the cost of not having one bag available when needed is $10.00.
We can use the normal distribution to estimate the probability of demand exceeding our inventory level. If we assume that demand follows a normal distribution with mean 150 and standard deviation 60, then we can calculate the probability of running out of inventory as
P(demand > inventory) = P(Z > (inventory - mean) / std_dev)
P(demand > inventory) = P(Z > (inventory - 150) / 60)
where Z is the standard normal random variable.
We want to choose the inventory level that minimizes the expected total cost, which is the sum of the cost of holding inventory and the cost of not having enough inventory
Expected total cost = cost of holding inventory + cost of not having enough inventory
Expected total cost = (inventory * $2.00) + (P(demand > inventory) * $10.00)
To minimize this cost, we need to find the inventory level that makes the expected total cost as low as possible. We can use calculus to find the minimum expected total cost.
Taking the derivative of the expected total cost with respect to the inventory level, we get
d/d(inventory) (Expected total cost) = $2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60)
Setting this derivative equal to zero and solving for the inventory level, we get
$2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60) = 0
Simplifying this equation, we get
exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60 = 0.2
Using a numerical solver or a table of values for the standard normal distribution, we can find that the inventory level that minimizes the expected total cost is approximately 174 bags.
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Please im really stuck (dont do bonus)
Step 1: Corresponding sides, AB = 2 units, BC = √(13) units, AC = 3 units, A'B'= 4 units, B'C' = √(52) units, C'A' = 6 units. Step 2: scale factor of dilation is 2. Bonus: 2√(13) units.
Describe Dilation?Dilation can be performed with respect to a fixed point called the center of dilation, or with respect to a fixed line called the line of dilation. When dilation is performed with respect to a point, the distance between the center of dilation and every point on the object is multiplied by the same scale factor. When dilation is performed with respect to a line, the distance between every point on the object and the line of dilation is multiplied by the same scale factor.
Step 1: Comparing corresponding sides
AB = distance between A(2,3) and B(2,1) = 2 units
BC = distance between B(2,1) and C(5,3) = √((5-2)² + (3-1)²) = √(9+4) = √(13) units
AC = distance between A(2,3) and C(5,3) = 3 units
A'B' = distance between A'(-4,-1) and B'(-4,-5) = 4 units
B'C' = distance between B'(-4,-5) and C'(2,-1) = √((-4-2)² + (-5+1)²) = √(36+16) = √(52) units
C'A' = distance between C'(2,-1) and A'(-4,-1) = 6 units
Step 2: Finding the scale factor
To find the scale factor, we need to divide the length of each corresponding side in triangle A'B'C' by the length of the corresponding side in triangle ABC. This gives us:
Scale factor = A'B' / AB = 4/2 = 2
So, the scale factor of dilation is 2.
Bonus: Finding the length of BC and B'C'
To find the length of BC and B'C', we can use the distance formula.
The length of BC = √((5-2)² + (3-1)²) = √(13) units.
The length of B'C' = √((-4-2)² + (-5+1)²) = √(52) units.
Alternatively, we could also use the scale factor to find the length of B'C':
B'C' = BC x scale factor = √(13) x 2 = 2√(13) units.
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Please someone answer this
The expression of radicals [tex]\sqrt{a + b}[/tex] = √a + √b is not possible because they have different root number.
What are radicals?A Radical is described as the symbol, '√' that is used to denote square root or nth roots.
Also, radical Expression is described as the radical expression containing a square root.
The rules in addition and subtraction of radicals are;
Only radicals with the same root number can be added or subtracted from each other. If the radicals in a question are unlike, you won't be able to combine them together.All exponents in the radicand must be less than the index.Any exponents in the radicand can have no factors in common with the index.No fractions appear under a radical.From the information given, we have that;
a ≠b
So, for the expression;
[tex]\sqrt{a + b}[/tex] = √a + √b,. it is not feasible
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Two wires lie perpendicular to the plane of the paper and carry equal electric currents in the direction shown. Point P is equidistant from the two wires.a) Construct a vector diagram showing the net magnetic field vector at point P. Explain your reasoning.b) Suppose a third wire carrying equal current into the plane of the paper were located at P. What would be the direction of the force on this wire? Explain your reasoning.
The net magnetic field at point P is zero, as the magnetic fields produced by the two equal currents in opposite directions cancel out. A third wire at P would experience zero force due to the net zero magnetic field at P.
To construct a vector diagram showing the net magnetic field vector at point P, we can use the right-hand rule for determining the direction of the magnetic field around a current-carrying wire.
If we curl the fingers of our right hand in the direction of the current in the first wire, which is out of the page, the thumb points in the direction of the magnetic field at point P due to the first wire. Similarly, in the opposite direction to the magnetic field at point P due to the second wire.
Since the magnetic fields they produce at P have equal magnitudes but opposite directions. Therefore, the net magnetic field at P is zero,
If a third wire carrying equal current into the plane of the paper were located at P, the direction of the force on this wire would be perpendicular to both the magnetic field produced by the other two wires and the direction of the current in the third wire.
Since the net magnetic field at P is zero, the vector product of the current in the third wire and the magnetic field is also zero, and there is no force on the third wire.
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