Answer:
(a) sin() = 1/2
degrees: 30, 150
radians: π/6, 5π/6
(b) sin() = − 1/2
degrees: 210, 330
radians: 7π/6, 11π/6
Note that these solutions are in the interval of 0 to 360 degrees or 0 to 2 radians. Also note that these are the primary solutions, there are infinitely many solutions that can be obtained by adding multiples of 360 degrees or 2π radians to these values.
A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population. T/F
A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population.
The following statement is True.
A variable is a trait that can be measured and has several values. Variables include height, age, income, province or country of birth, school grades, and kind of dwelling. Variables can be divided into two types: category and numeric.
A "sampling frame" is a list of all population items to be researched. Probability and nonprobability are the two primary types of sampling methodologies. A simple random sample is a sample drawn from the population in which every member has an equal probability of being chosen.
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Find the value of X and the length of YZ
Answer: x = 8 and YZ = 19
Step-by-step explanation:
mb i focused on the x between a and y and i forgot the x they were talking about was the x in the equations..
since its a bisector, we know that az = yz therefore 2x + 3 = 3x - 5
2x + 3 = 3x - 5
2x + 8 = 3x
8 = x
now we know the value of x, we can plug it into the equation for yz
3(8) - 5
24 - 5
19
therefore, x = 8 and yz = 19
HELP FAST WILL GIVE BRAINLYS IF ANSWER IS RIGHT!
You work in a dentist’s office. You record the number of X-ray plates used each day of the week that the dentist works, as shown: 15, 13, 16, 18, 13, and 22. The dentist then calculates the mean by dividing the number of X-ray plates used (97) by the number of days in the week (5).
What was the dentist’s mistake in the calculation?
The dentist counted 13 twice.
The dentist counted too few days.
The dentist counted too many days.
The dentist divided instead of multiplying.
The dentist did not sum the number of plates used correctly.
Answer:
Dentist counted to few days.
Step-by-step explanation:
if you invest $360 and your annual intrest is $54, what is the intrest rate
Answer:
15%
Step-by-step explanation:
The answer is the answer.
Show that the triangles are similar and write a similarity statement.
Answer:
im sorry bro i
Step-by-step explanation:
i just need points
K
A deli owner has room for 55 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total
of 400 oz of cheese. If 5-oz containers sell for $9 and 10-oz containers sell for $17, how many of each should he sell to
maximize his revenue? What is his maximum revenue?
He should sell 5-oz containers and 10-oz containers to maximize his revenue.
Answer:
$630
Step-by-step explanation:
This problem can be solved using linear programming. Let x be the number of 5-oz containers and y be the number of 10-oz containers. The constraints are:
x + y = 55 (total number of containers)
5x + 10y = 400 (total amount of cheese in ounces)
x >= 0, y >= 0 (containers must be non-negative)
The objective is to maximize the revenue, which is given by 9x + 17y.
Using a linear programming solver, we find that the maximum revenue is obtained when x = 40 and y = 15. The maximum revenue is 9x + 17y = 9 * 40 + 17 * 15 = $630.
So, the deli owner should sell 40 5-oz containers and 15 10-oz containers to maximize his revenue, which is $630.
HELPP!!!!
The scale of a map is 1 inch : 6 miles. If your house is 78 miles from the airport, how many
inches will that be on your map?
Answer:
The scale of a map tells you the relationship between the distance on the map and the actual distance in real life. In this case, the scale of the map is 1 inch : 6 miles, which means that 1 inch on the map represents 6 miles in real life.
To find out how many inches on the map 78 miles represents, you can use the following formula:
distance on the map = distance in real life / scale
So in this case:
distance on the map = 78 miles / 6 miles/inch
distance on the map = 78/6 inches
So 78 miles from the airport will be 13 inches on the map.
As part of a survey, 300 girls were asked to name their favorite sport. 12 of the girls named bowling as their favorite. Based upon the results, how many of the next 200 girls surveyed would you expect to choose bowling as their favorite sport?
The number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.
What is percentage?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given that 300 girls were asked to name their favorite sport. 12 of the girls named bowling as their favorite.
The percentage of girls that selected the sport is thus:
12/ 300 (100) = 4%
For the next 200 girls, calculate the 4% of the number to get the number of girls who like bowling:
200 (4%) = N
N = (200)(4/100)
N = 8
Hence, the number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.
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Please help me with this question.
The solution of the equation can be obtained as x = 1.
How do we solve the exponential equation?
We have to note that the exponential equation can be solved in the form of a quadratic equation and then we can be able to obtain the values that can be able to sort out the equation.
We know that;
e^2x + e^x - 12= 0
Let p represent e^x we would then have
p^2 + p - 12 = 0
If we solve the quadratic we would have;
p = 3 or p = -4
If we discard the negative answer;
e^x = 3^1
x = 1
The solution of the equation x = 1.
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Based on the completed Form 1040 and 2018 Taxable Income Tiers, what is the total tax
that the employee is responsible for paying?
Answer in complete sentences.
By assuming that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be: $17,836.
What are tax bracket or income tiers?A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.
In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.
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Which line has a constant of proportionality between y and x of 3?
A system has three computers. Computer 1 works with a probability of 0.65; computer 2 works with a probability of 0.65; computer 3 works with a probability of 0.87. Suppose that the operations of the computers are independent of each other. Suppose that the system works only if at least one computer is working. What is the probability that the system works? Round your answer to four decimal places.
Probability that the system works is approximately 0.9841.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Let the three events be C₁, C₂ and C₃.
Probability that computer 1 works = P(C₁) = 0.65
Probability that computer 1 does not work = P(C₁') = 1 - 0.65 = 0.35
Probability that computer 2 works = P(C₂) = 0.65
Probability that computer 2 does not work = P(C₂') = 1 - 0.65 = 0.35
Probability that computer 3 works = P(C₃) = 0.87
Probability that computer 3 does not work = P(C₃') = 1 - 0.87 = 0.13
Let the event that at least one of the computer is working is S.
P(S) = 1 - P(no computer is working)
P(no computer is working) = P(C₁' ∩ C₂' ∩ C₃')
We have the operations of the computers are independent of each other.
P(C₁' ∩ C₂' ∩ C₃') = P(C₁') × P(C₂') × P(C₃')
= 0.35 × 0.35 × 0.13
= 0.015925
P(no computer is working) = 0.015925
P(S) = 1 - 0.015925
= 0.984075 ≈ 0.9841
Hence the required probability is 0.9841.
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A ∪ B ∪ C
A union B union C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
A ∪ B ∪ C is the set of all items in sets A, B, or C.
Region V: Items in A, B, and C
What does A ∪ B ∪ C represent?In set theory, the union of two or more sets is a new set that contains all the elements from each of the original sets. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∪ B = {1, 2, 3, 4}.
In this case, A ∪ B ∪ C represents the set of all elements that belong to at least one of the sets A, B, or C.
Therefore, A ∪ B ∪ C represents the set of all items in sets A, B, or C.
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Martinez Company’s relevant range of production is 7,500 units to 12,500 units. When it produces and sells 10,000 units, its average costs per unit are as follows:
Average Cost per Unit
Direct materials $ 6.00
Direct labor $ 3.50
Variable manufacturing overhead $ 1.50
Fixed manufacturing overhead $ 4.00
Fixed selling expense $ 3.00
Fixed administrative expense $ 2.00
Sales commissions $ 1.00
Variable administrative expense $ 0.50
3. If 8,000 units are produced and sold, what is the variable cost per unit produced and sold?
The variable cost per unit produced and sold is, $11.50
What is average?In mathematics, Average is a value which we calculate by dividing the sum of values of all the data-set by the number of data-sets.
Average = sum of values of all the data-set/number of data-sets
The variable cost per unit produced and sold can be calculated by summing up the costs that vary with changes in production volume, and dividing the total by the number of units produced and sold.
For Martinez Company, the variable costs per unit are:
Direct materials = $ 6.00
Direct labor = $ 3.50
Variable manufacturing overhead = $ 1.50
Variable administrative expense = $ 0.50
Total variable cost per unit = $6.00 + $3.50 + $1.50 + $0.50
= $11.50
So, if 8,000 units are produced and sold, the variable cost per unit produced and sold would be $11.50.
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Cinema A sells a twelve-pack of movie passes for $66. Cinema B sells a five-pack of movie passes for $29. Find the unit cost for each movie pack and determine.
The unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.
How to determine the unit ratesTo find the unit cost of each movie pack, we need to divide the total cost by the number of passes in each pack.
The unit cost for Cinema A's twelve-pack can be calculated as follows:
unit cost for Cinema A = $66 / 12 passes = $5.50 per pass
The unit cost for Cinema B's five-pack can be calculated as follows:
unit cost for Cinema B = $29 / 5 passes = $5.80 per pass
So, the unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.
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What is the domain of the graph
below?
Answer:
A
Step-by-step explanation:
[tex]4\leq x < 4[/tex]
Focusing on the left end of the graph, the x value corresponding to the graph is -4. The circle present at this end of the graph is coloured in, which indicates that -4 is included in the domain.
Focusing on the right end of the graph, the x value corresponding to the graph is 4. The circle present at this end of the graph is NOT coloured in, which indicates that 4 is NOT included in the domain.
The graph shows the temperature of heated water at a certain heating time. What are the variables? Describe how the variables are related at various points on the graph.
The variables in the graph are temperature of the water (y-axis) and heating time (x-axis).
What are the variables?At various points on the graph, the relationship between the two variables can be seen as a linear increase in temperature with a corresponding increase in heating time. That is, as the heating time increases, the temperature of the water also increases.
The graph shows the relationship between two variables, heating time and temperature of heated water. The x-axis, or independent variable, represents the heating time, while the y-axis, or dependent variable, records the temperature of the heated water.
At the start of the graph, the heating time is 0 minutes and the temperature of the heated water is also 0 degrees Celsius. As the heating time increases, the temperature of the heated water gradually increases. At 10 minutes, the temperature of the heated water is approximately 20 degrees Celsius.
At 20 minutes, the temperature of the heated water is approximately 50 degrees Celsius. At 30 minutes, the temperature of the heated water is approximately 80 degrees Celsius. At 40 minutes, the temperature of the heated water is approximately 100 degrees Celsius and at 50 minutes, the temperature of the heated water is approximately 120 degrees Celsius.
The relationship between the two variables is linear; as the heating time increases, the temperature of the heated water also increases. The graph shows that the temperature of the heated water increases by approximately 20 degrees Celsius for every 10 minutes of heating time.
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PLEASE HELP ME!
Going into the final exam, which will count as two tests, Sharon has test scores of 77, 84, 72,65, and 96. What score does Sharon need on the final in order to have an average score of 80 ?
On the final, the score that Sharon would need to have in order to have the average score of 80 is 3.
How to solve for the scoreLet's call the score Sharon needs on the final exam "x".
The total of all 6 test scores is: 77 + 84 + 72 + 65 + 96 + x
The average of all 6 test scores is: (77 + 84 + 72 + 65 + 96 + x) / 6 = 80
Expanding and solving for x, we have:
77 + 84 + 72 + 65 + 96 + x = 80 * 6
477 + x = 480
Subtracting 477 from both sides, we get:
x = 480 - 477
x = 3
So, Sharon needs a score of 3 on the final exam in order to have an average score of 80.
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Find the equation of the line passing through the points (8, -16) and (1, 5).
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{8}}} \implies \cfrac{5 +16}{-7} \implies \cfrac{ 21 }{ -7 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{8}) \implies y +16 = - 3 ( x -8) \\\\\\ y+16=-3x+24\implies {\Large \begin{array}{llll} y=-3x+8 \end{array}}[/tex]
Prove that every non-empty finite set of positive integers contains a least element, by induction on n the size of the set.
The statement can be proven using mathematical induction. Let S be a non-empty finite set of positive integers.
Base case: If n = 1, then the only element in S is the least element.
Inductive step: Assume that the statement holds for all sets S of size n. Now, consider a set S of size n + 1. If a is the least element of S, then the set S' = S \ {a} has size n and, by the induction hypothesis, contains a least element b. Since a is the least element of S, it follows that b ≤ a. Then, either a = b or a < b.
If a = b, then a is the least element of S.If a < b, then b is the least element of S.Therefore, in any case, S contains at least element. This completes the proof by induction.
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FInd the lenghxwidth of randys living room
Answer:
150
Step-by-step explanation:
If the length of the living room is 10, and the width is 15, then we can use the equation:
10 × 15 = 150
Therefore, the length × width of the living room is 150.
The population of a certain town is 158,260 and increases exponentially at the rate of 6% every year. Which equation best represents the population after x years?
The equation for the population after x years can be represented using P(x) = 158,260 * (1 + 0.06)^x
Which equation best represents the population after x years?From the question, we have the following parameters that can be used in our computation:
Initial, a = 158260
Rate, r = 6%
The function is represented as
P(x) = a(1 + r)^x
This means that
P(x) = 158,260 * (1 + 0.06)^x
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A new appliance salesperson sold an average of $12,000 per day for the first 3 days they worked.
On the next 4 days they worked, they sold an average of $9,000 per day. How much did they sell on average per day over the entire 7 days?
Kelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $12 per hour by the store. In the evening she works at a restaurant as a manager for 5 hours and is paid $20 per hour. How much does she make on average per hour for the day?
7. Henry worked for 10 consecutive days, earning an average wage of $120 per day at his dog walking business. During the first 5 days, Henry averaged $100 per day and his average earned for the next 4 days was $130 per day. How much did he earn on the last day?
Marcus has a slugging average of .484 and has had 18 singles, 33 doubles, 2 triples, and 54 homeruns. How many at-bats has Marcus had?
It is Tyler's first season playing baseball with the Diamondbacks. He has had 383 at-bats. So far, he has 74 singles, 13 doubles, 11 triples and 4 homeruns. What is Tyler's current Slugging Percentage? What is Tyler's Batting Average?
Tyler's current Slugging Percentage is 546 and current Batting Average is 192.
What is Slugging Percentage?Slugging percentage is a statistic used in baseball and softball to measure a batter's total number of bases per at bat. It is calculated by dividing the total number of bases earned by the number of at-bats. This statistic is often used to compare batters since it takes into account the number of bases earned in addition to the number of hits. Slugging percentage is an important statistic to consider when evaluating batters since it provides an overall picture of how well a batter is performing. Slugging percentage is usually expressed as a decimal or a percentage, with a higher percentage indicating better performance.
Tyler's current Slugging Percentage is .546. This is calculated by adding the total number of bases earned (74 + 2*13 + 3*11 + 4*4 = 194) and dividing that by the total number of at-bats (383).
Tyler's current Batting Average is .192. This is calculated by dividing the total number of hits (74 + 13 + 11 + 4 = 102) by the total number of at-bats (383).
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Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
15 yd
5 yd
6 yd
Syd
7 yd
According to the problem the missing side length is 7 yd.
What is length?Length is a concept used in various contexts to measure the size of an object or distance between two points. In geometry, length refers to the longest dimension of an object. In physics, length is a fundamental quantity that is used to measure the distance between two points. It is usually expressed in units such as meters, centimeters, and millimeters.
The missing side length is 7 yd. This is because the shape formed by these sides is a right triangle, and the Pythagorean theorem can be used to calculate the length of the missing side. The equation is [tex]a^{2} +b^{2} =c^{2}[/tex], where a and b are the two known side lengths and c is the missing side length. In this case, a = 6 yd and b = 8 yd, so [tex]c^{2} = 6^{2} +8^{2} =100[/tex]. The square root of 100 is 10, so c = 10 yd.
However, since the question asks for the missing side length in yards, the answer is 7 yd (10 yd divided by 1.4 to convert to yd).
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Please help me with this
Extra points
The equation that represents the second step of solution process is 12x-3+27=-24. Thus, option A is correct.
What is simplex method of equation ?The simplex method is a widely used linear programming methodology for addressing optimization problems. These problems typically involve a function and a number of constraints that are stated as inequalities.
Step 1: 3(4x-1)+27=-24
Step 2: 12x-3+27=-24
Step 3: 12x+24=-24
Step 4: 12x=-48
Step 5: x=-4
A. 12x-3+27=-24.
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The movies charges 16$ for adults and 16$ for children. The revenue total was 672$ determine the number of each tickets sold if the number of children tickets sold was half the number of the adults.
Answer:
7 child tickets
14 adult tickets
Step-by-step explanation:
Let a = the number of adult tickets
Let c = the number of child tickets
16a + 16c + 672
2c = a Substitute 2c for a
15a + 16c = 672
16(2a) + 16c = 672
32a + 16c = 672 Combine like terms
48a = 672 Divide both sides by 48
a = 14
2c = a
2c = 14 Divide both sides by 2
c = 7
Which graph shows the solution to the system of linear equations? y equals one third times x x + 3y = 6 coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1 coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3
The graph that shows the solution to the system of linear equations is the coordinate plane with the lines that pass through the points (0, 0), and (2, 1) and another line (0, 4), and (-1, 1).
What is the system of linear equations?
A system of linear equations is a set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.
The graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0, 0, and 2, 1 and another line that passes through the points 0, 4, and -1, 1.
When two lines intersect, their point of intersection is the solution to the system of linear equations.
In this case, the point of intersection is (2, 1) which means x = 2 and y = 1.
Hence, The graph that shows the solution to the system of linear equations is the coordinate plane with the lines that pass through the points (0, 0), and (2, 1) and another line (0, 4), and (-1, 1).
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help asap its timed cmon
When the center angle is 60 degrees, the arc length is measured in 1.047 units.
What is arc?An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference. An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference. An arc is a kind of curve.
Here,
angle=60°
in triangle BCD,
cos 60=CB/DB
DB= 2 units
radius=1 unit
arc length=2πr*(θ/360)
=2*3.14*1*60/360
=1.047 units
The measure of arc length when central angle is 60 degree is given by 1.047 units.
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Pls answer the following question of " Solving for the variables" using the attachment below:
The values of the variables are b = 90, c = 80 and d = 100
How to determine the variablesFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
Using the properties of parallelogram, we have the following equations
b - 10 + b + 10 = 180
d = b + 10
c = b - 10
Solving the first equation, we have
2b = 180
So, we have
b = 90
This means that
d = 90 + 10 = 100
c = 90 - 10 = 80
Hence, the value of d is 100 degrees
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Find an expression which represents the sum of (-4x-7)and (6x-4)in simplest terms
The expression that represents the sum of ( -4x - 7 ) and ( 6x - 4 ) in simplest terms is 2x - 11
What is the sum of the two expression?Given the expressions in the question;
( -4x - 7 ) and ( 6x - 4 )
To find the sum of the two expression, replace the 'and' with '+' and simplify.
( -4x - 7 ) and ( 6x - 4 )
( -4x - 7 ) + ( 6x - 4 )
-4x - 7 + 6x - 4
Collect like terms
-4x + 6x - 4 - 7
Add -4x and 6x
2x - 4 - 7
Add -4 and -7
2x - 4 - 7
2x - 11
Therefore, the simplified form of the expression is 2x - 11
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