angle A and Angle B are supplementary angles. if the measure of angle B is 20 less than 3 times the measure of angle A, find the measurement of angle B.
Answers
Answer:
∠ B = 130°
Step-by-step explanation:
given ∠ B = 3 ∠ A - 20
supplementary angles sum to 180°
sum A and B and equate to 180
∠ A + 3 ∠ A - 20 = 180
4 ∠ A - 20 = 180 ( add 20 to both sides )
4 ∠ A = 200 ( divide both sides by 4 )
∠ A = 50
that is ∠ A = 50° and
∠ B = 3 ∠ A - 20 = 3 × 50 - 20 = 150 - 20 = 130°
Related Questions
For problems 1 and 2, What is the most precise classification of the quadrilateral?
1.F(−13,7),I(1,12),N(15,7),E(1,−5)
2.Q(4,5),U(12,14),A(20,5),D(12,−4)
Answers
Are you given does types of quadrilateral
because if not you won't be able to answer the question
But if you are given send them and will take it from the
a factory uses a part they ordered from three different suppliers (A,B,C) . the supplier have efective rate of 1.21% , 4.75& , 5.1% respectively. A container has 40% of supplier A, 24% of supplier B and the rest from supplier C. for a random selection , what is the probability of ;
a) Being ordered from supplier C?
b)being defective ?
c) being defective and being ordered from supplier C?
d) being defective given it has been ordered from C?
e) being ordered from supplier C given it is defective?
Answers
a) Probability of being ordered from supplier C = 36%
b) Probability of being defective = 2.69%
c) Probability of being defective and being ordered from supplier C = 0.9684%
d) Probability of being defective given it has been ordered from C = 2.69%
e) Probability of being ordered from supplier C given it is defective ≈ 35.97%
To solve the probability questions, let's break them down one by one:
a) The probability of being ordered from supplier C can be calculated by finding the percentage of the container that comes from supplier C. We know that supplier C provides the remaining portion of the container, which is 100% - (40% + 24%) = 36%. Therefore, the probability of being ordered from supplier C is 36%.
b) To calculate the probability of being defective, we need to consider the effective rates of each supplier. The effective rate of supplier A is 1.21%, supplier B is 4.75%, and supplier C is 5.1%. We can calculate the overall probability of being defective by taking the weighted average of the defect rates based on the proportion of each supplier in the container:
Probability of being defective = (40% * 1.21% + 24% * 4.75% + 36% * 5.1%) = 2.69%
c) The probability of being defective and being ordered from supplier C can be calculated by multiplying the probability of being defective (from part b) with the probability of being ordered from supplier C (from part a):
Probability of being defective and ordered from supplier C = Probability of being defective * Probability of being ordered from supplier C
= 2.69% * 36% = 0.9684%
d) To calculate the probability of being defective given it has been ordered from supplier C, we need to find the conditional probability. In this case, we consider the probability of being defective among the items that have been ordered from supplier C. The probability of being defective given it has been ordered from supplier C can be calculated using the following formula:
Probability of being defective given it has been ordered from C = (Probability of being defective and ordered from C) / (Probability of being ordered from C)
= 0.9684% / 36% = 2.69%
e) To find the probability of being ordered from supplier C given that it is defective, we need to calculate the conditional probability. It represents the likelihood of the item being ordered from supplier C, given that it is defective. The probability of being ordered from supplier C given it is defective can be calculated using the formula:
Probability of being ordered from C given it is defective = (Probability of being defective and ordered from C) / (Probability of being defective)
= 0.9684% / 2.69% ≈ 35.97%
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A computer technician charges customers $75 per hour.
Let h represent the number of hours the technician works.
o f(h) = 75 + h
o f(h) = 75 + h
Of(h) = 75h
Of(h) = 75 - h
Answers
Answer:
C. f(h)=75h
Step-by-step explanation:
That is the answer, hope it helps!
Answer:
it is the first one f(h)=75+h
The function h(t) = −16t2 + 48t + 36 models the height of a ball, in feet, at t seconds after being thrown into the air.
Part A
What feature of the function represents the highest point of the ball?
A. end behavior
B. symmetry
C. vertex
D. zero
Part B
What is the highest point of the ball, in feet?
Answers
calculate the volume of water in the ocean in liters
Answers
The volume of water in the ocean is estimated to be approximately 1,332,000,000,000,000,000 liters.
The Earth's oceans cover about 71% of the planet's surface and contain a vast amount of water. To calculate the volume of water in the ocean, we need to consider the average depth and the total surface area of the oceans.
The average depth of the ocean is estimated to be around 3,800 meters. The total surface area of the oceans is approximately 361,900,000 square kilometers. By multiplying the average depth by the surface area, we can find the volume of water.
Volume = Average Depth × Surface Area
Using the given values, we have:
Volume = 3,800 meters × 361,900,000 square kilometers
To convert this volume to liters, we need to consider that 1 cubic meter is equal to 1,000 liters. Therefore, we can multiply the volume in cubic meters by 1,000 to obtain the volume in liters.
Calculating the above expression, we find that the volume of water in the ocean is approximately 1,332,000,000,000,000,000 liters. This is an estimation and may vary slightly depending on the sources and assumptions used for average depth and surface area calculations.
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Graph a line with a slope of 4 that contains the point (3,0)
Answers
\(\huge\fbox{Hello\:there!}\)
We are given the slope of the line and a point that it passes through.
So, we can use the Point-Slope Formula:
\(\rm{y-y1=m(x-x1)\)
Where y1 is the y-coordinate of the point, m is the slope of the line, and x1 is the x-coordinate of the line.
Now, plug in the values:
\(\rm{y-0=4(x-3)\)
\(\rm{y-0=4x-12\)
\(\rm{y=4x-12\) (the equation of the line in slope-intercept form)
Now, how to graph it?
First of all, the y-intercept is (0, -12)
Remember, y-intercepts always have an x-coordinate of 0.
Now, 4 is the slope (Rise/Run)
Where Rise is how many units we move up or down, and Run is how many units we move left or right.
In this case, we move 4 up, over 1, up 4, over 1, and so on, until we have a line.
Then all we have to do is take a ruler and connect the points. :)
Hope you find it helpful.
Feel free to ask if you have any doubts.
\(\bf{-Sparkles^**^*^\)
Can someone please help me
Answers
Answer:-2.4+3.2t
Step-by-step explanation:
-3.6+1.2-1.9t+5.1t
= -2.4+3.2t
10. What is 4/5 x 3/7?
Answers
Answer:
12/35
Step-by-step explanation:
you have to just multiply across
\( \frac{4}{5} \times \frac{3}{7} = \frac{12}{35} \)
The answer as a fraction is 12/35
The answer as a decimal is 0.343
URGENT PLZ!! Drag the correct transformation into the box to match the definition. [BLANK]... moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding preimage and image points. Translation Rotation Reflection
Answers
Answer:
Reflection.
Step-by-step explanation:
Reflection moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding pre-image and image points.
On the other hand, "Translation" moves points the same distance along lines that are parallel to each other while "Rotation" moves points along concentric circles and through the same angle of rotation.
At an angle of 90°, a line of reflection intersects the line segments connecting corresponding points of the pre-image under a reflection.
Basically, a reflection allows us to flip an object or figure across a line, point or plane without any change in its shape or size.
Hence, to reflect an object or a figure such as a triangle simply means that its mirror image would be produced with respect to a line; this line is generally referred to as the line of reflection.
which structure is found in the cytoplasm of a typical plant cell?
Answers
Answer:
Lysosomes
Step-by-step explanation:
A force of 25 N will stretch a spring 55 cm(0.55 m). Assuming Hooke's law applies, how far will a 80−N force stretch the spring? How much work does it take to stretch the spring this far?
Answers
It takes approximately 84.9 J of work to stretch the spring 1.76 m.
Hooke's law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be expressed as:
F = kx
where F is the applied force, x is the displacement of the spring from its equilibrium position, and k is the spring constant.
To find the spring constant k, we can use the given information that a force of 25 N stretches the spring 55 cm (0.55 m):
F = kx
25 N = k(0.55 m)
k = 25 N / 0.55 m
k = 45.45 N/m
Now we can use Hooke's law to find how far an 80-N force will stretch the spring:
F = kx
80 N = 45.45 N/m * x
x = 1.76 m
Therefore, an 80-N force will stretch the spring by 1.76 m.
To find the work required to stretch the spring this far, we can use the formula:
W = (1/2)kx^2
where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
Substituting the given values, we get:
W = (1/2) * 45.45 N/m * (1.76 m)^2
W = 84.9 J
Therefore, it takes approximately 84.9 J of work to stretch the spring 1.76 m.
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A gas turbine is used to generate electricity. It can be modelled as a cycle utilising air as the working fluid. The air is initially compressed in a two stage compressor from 1 bar to 16 bar. The air is initially at 32"C. Between the two stages of the compressor, there is an intercooler which reduces the temperature to 32°C. It may be assumed that the two stages of the compressor have an equal pressure ratio. The compressed gas then passes to a heat exchanger, which models the combustion chamber, where it is heated to 1500'C. The hot gases are then expanded through a turbine to extract work, and the exhaust gases vented at 1 bar. It may be assumed throughout that all rotating machinery has an isentropic efficiency of 90% What are the advantages and disadvantages of using a multi-stage compressor over a single stage? [2] ) How are the isentropic efficiencies of a compressor and a turbine defined? [2] (i) For an isentropic process on a perfect gas, it can be shown that pr constant. Starting from this expression, show that: T: T: [4] () For this cycle, calculate the back work ratio and the thermal efficiency. How does this compare with the maximum efficiency possible for this cycle? How could you improve the thermal efficiency of this process? [12] Data: For air: Cp 1.15 kJ/kg Ky 1.33 P.
Answers
The advantages of using a multi-stage compressor over a single stage include higher overall pressure ratios, improved efficiency, and better performance. The division of compression into multiple stages allows for lower pressure ratios per stage, reducing the workload and enabling better control. Intercooling between stages further enhances efficiency. However, multi-stage compressors are more complex, expensive, and have a higher risk of operational issues.The main disadvantages of using a multi-stage compressor are increased complexity, higher costs, and a greater potential for operational issues compared to single-stage compressors.
Advantages and disadvantages of using a multi-stage compressor over a single stage:
The main advantage of a multi-stage compressor is its ability to achieve higher overall pressure ratios, leading to improved efficiency and performance. By dividing the compression process into multiple stages, each stage operates at a lower pressure ratio, reducing the workload on each stage and allowing for better control and optimization. Additionally, intercooling between stages can help lower the temperature and improve efficiency further. However, multi-stage compressors are more complex and expensive than single-stage compressors, requiring additional equipment, maintenance, and space. They also introduce more potential points of failure, increasing the risk of operational issues.
Isentropic efficiencies of a compressor and a turbine are defined as follows:
The isentropic efficiency of a compressor is the ratio of the actual work input to the ideal work input, assuming an isentropic (reversible adiabatic) process. It represents the efficiency with which the compressor raises the pressure of the working fluid.
The isentropic efficiency of a turbine is the ratio of the actual work output to the ideal work output, assuming an isentropic process. It represents the efficiency with which the turbine extracts work from the working fluid.
Starting from the expression pr constant (pressure ratio constant), we can derive the relationship between temperatures at different points in an isentropic process. By applying the ideal gas law and rearranging the equation, we obtain the relationship T1/T2 = (P1/P2)^((k-1)/k), where T1 and T2 are the temperatures at points 1 and 2, and P1 and P2 are the pressures at points 1 and 2, respectively. This equation shows that the temperature ratio is related to the pressure ratio by the specific heat ratio (k) of the gas.
To calculate the back work ratio and thermal efficiency for the given cycle, we need to determine the specific heat capacity (Cp), specific gas constant (R), and specific heat ratio (k) of the air. With these values, we can calculate the back work ratio (BWR) as the ratio of the work required for compression to the work produced by the turbine. The thermal efficiency (ηth) is the ratio of the net work output to the heat input.
To improve the thermal efficiency of this process, several approaches can be considered. One option is to increase the intercooling efficiency to reduce the temperature at the compressor inlet. Another possibility is to enhance the combustion process to achieve higher temperatures and better combustion efficiency. Additionally, improving the turbine's isentropic efficiency would increase the work output. Utilizing waste heat recovery techniques, such as a bottoming cycle or combined heat and power (CHP) systems, can also boost the overall thermal efficiency by utilizing the heat from the exhaust gases for additional purposes.
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B. outline 5 possible terminal problems and 5 solutions. (10 marks)
Answers
Terminal problems refer to critical issues or challenges that can have severe consequences and require immediate attention. Addressing these terminal problems requires a multi-faceted approach involving governments, organizations, and individuals working together to implement effective solutions and create a more sustainable and secure future.
1. Environmental degradation: The degradation of ecosystems, pollution, and climate change pose a significant terminal problem. Solutions include promoting sustainable practices, reducing greenhouse gas emissions, and investing in renewable energy sources.
2. Global poverty and inequality: Widespread poverty and inequality can lead to social unrest and instability. Solutions involve implementing fair economic policies, providing access to education and healthcare, and promoting inclusive growth.
3. Nuclear proliferation: The proliferation of nuclear weapons increases the risk of conflicts and catastrophic events. Solutions include diplomatic negotiations, arms control agreements, and non-proliferation treaties.
4. Cybersecurity threats: The increasing dependence on technology exposes societies to cyber-attacks and data breaches. Solutions involve strengthening cybersecurity measures, promoting awareness and education, and international cooperation in combating cyber threats.
5. Pandemics and health crises: Outbreaks of diseases and pandemics can have devastating consequences. Solutions include investing in healthcare infrastructure, strengthening global health systems, early detection and response mechanisms, and promoting international collaboration in research and development.
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The value of y varies directly with x. If x = 3, then y = 4. What is the value of x when y = 120 ?
Answers
Answer:
x = 90
Step-by-step explanation:
If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120
which is 30.
so just multiply 30 for x = 3, then the answer will be 90
x = 90
Answer:
x=90
Step-by-step explanation:
x is directly proportional to y
Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.
Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.
Can anyone help me with this one
Answers
Answer:
12n+9=93
solve for n
12n=93-9
n=84/12
n=7
therefore, Mr. copper bought 7 tickets.
daniel earns extra money as a lifeguard he earns 37 dollars for 4 hours and 64.75 for 7 hours. the relationship between his earnings and the time worked is proportional true or false?
Answers
Answer: Yes, it is proportional.
Step-by-step explanation:
Find the amount Daniel earns each hour.
Divide the amount of money by the number of hours to find each earnings per hour.
Life guard: $37 for 4 hours.
37/4 = 9.25
64.75/ 7 = 9.25
Since Daniel receives the same amount of money per hour which is $9.25 per hour, then the relationship is proportional.
Use the equation below to find T, if w = 76, m= 7, and a=4. T=wma
Answers
Answer:
2128
Step-by-step explanation:
T=wma T=76 X 7 X 4=2128
Answer:
T = 2128
Step-by-step explanation:
Step 1: Define equation
T = wma
w = 76
m = 7
a = 4
Step 2: Substitute
T = 76(7)(4)
Step 3: Evaluate
T = 2128
please answer this!!
Answers
which image shows -1 7/8 on a number line
Answers
Answer:
C
Step-by-step explanation:
C goes past -1 and almost reaches -2 so you know it will include some sort of fraction.
If you count the tick marks, C is on the 7th tick mark which is the one before -2. This represents 7/8 because 8/8 would be right on -2.
So, C shows -1 and 7/8
0.545
Convert to fraction
Answers
Answer:
109/200
Step-by-step explanation:
There are 10 people taking part in a raffle.
Ann, Bob, Elsa, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.
Suppose that prize winners are randomly selected from the 10 people.
Compute the probability of each of the following events.
Event A: The first three prize winners are Soo, Ann, and Jim, regardless of order.
Event B: Ann is the first prize winner, Lena is second, and Bob is third.
Write your answers as fractions in simplest form.
P(A) =
?
P (B) =
Answers
The probabilities are:
\(P(A) = \frac{1}{120}\) and \(P(B) = \frac{1}{720}\).
To calculate the probabilities, we need to consider the total number of possible outcomes and the number of favorable outcomes for each event.
Event A: The first three prize winners are Soo, Ann, and Jim, regardless of order.
There are 10 people, so the total number of possible outcomes is 10P3 (permutations of 10 people taken 3 at a time).
This is calculated as 10! / (10-3)! = 10! / 7! = 10 * 9 * 8 = 720.
The number of favorable outcomes is 3! (permutations of 3 people), as the order doesn't matter.
So, the number of favorable outcomes is 3! = 3 * 2 = 6.
P(A) = favorable outcomes / total outcomes = 6 / 720 = 1 / 120.
Event B: Ann is the first prize winner, Lena is second, and Bob is third.
Similarly, there are 10P3 total outcomes, which is 720.
The number of favorable outcomes is 1, as there is only one specific arrangement where Ann is first, Lena is second, and Bob is third.
P(B) = favorable outcomes / total outcomes = 1 / 720.
Therefore, the probabilities are:
P(A) = 1 / 120
P(B) = 1 / 720.
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What is the balance after 2 years in a savings account that earns 8% interest compounded biweekly (every two weeks) when the initial deposit is 12000?
Answers
The balance in the savings account after 2 years of compounding bi-weekly with a rate of 8% is 14.
The principal amount = 12000
The time period for which the compound interest is to be calculated = 2 years.
The rate of interest = 8%
The interest is compounded bi-weekly.
We need to find the balance after 2 years.
What is compound interest?Compound interest is the interest calculated on the principal and interest together for a given time period.
The formula used to calculate the amount when interest is compounded:
\(P(1+\frac{r}{n})^{nt}\\ Where~n~is~the~number~of~times~the~interest~is~compounded~annually\\r=rate~of~interest\\t=time~period.\)
We have,
P = 12000
T= 2 years
R = 8%
Compounded bi-weekly means every two weeks = 14 days
In a year we have 365 so we have around 52 weeks.
The number of 2-weeks in a year :
365 / 14 = 26.
We have, n = 26.
Putting P = 1200, T = 2, R = 8% and n = 26 in the amount of compound interest formula.
We get,
\(12000(1+\frac{8/100}{26})^{26\times2}\\12000(1+\frac{0.08}{26})^{52}\\12000(1+0.00307)^{52} \\12000(1.00307)^{52}\\12000\times1.172\\14,078\)
Rounding to the nearest whole number.
Amount / balance = 14.
Thus the balance in the saving account after 2 years of compounding bi-weekly with a rate of 8% is 14
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A bag contains 25 cards bearing number 1, 2, 3 …., 25 respectively. One card is drawn at random. What is the probability that number is divisible by 3?
pls help
Answers
Answer:
8/25
Step-by-step explanation:
there are 8 numbers from 1 - 25 that are divisible by 3 because 25/3 = 8.3333..
Written out these would be:
3,6,9,12,15,18,21, and 24
so you ahve 8 out of a total of 25
The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis?
Answers
Answer:
B. 7−10; 11−14; 15−18; 19−22
Step-by-step explanation:
Distance between skew lines Find the distance between the line L1 through the points A(1, 0, -1) and B(-1, 1, 0) and the line L2 through the points C(3, 1, -1) and D(4, 5, -2). The distance is to be measured along the line Perpendicular to the two lines. First find a vector n perpendicular to both lines. Then project rAC onton.
Answers
The distance between the two skew lines that measure along the line Perpendicular to the two lines is \(\frac{13}{\sqrt{70}}\).
To find the distance between the skew lines and measure the distance along the line perpendicular to the two lines, it is necessary to find a vector n perpendicular to both lines. Then project rAC onto that vector.
Here's the step-by-step explanation:
Step 1 Finding vector AB and vector CD
AB = vector B - vector A = (-1 - 1)i + (1 - 0)j + (0 + 1)k = -2i + j + kCD = vector D - vector C = (4 - 3)i + (5 - 1)j + (-2 + 1)k = i + 4j - kStep 2 Finding the vector n perpendicular to both lines.
The vector that is perpendicular to both lines is the cross-product of the vectors AB and CD.
n = AB x CD = (-2i + j + k) x (i + 4j - k) = -5i - 3j - 6kStep 3 Finding the projection of rAC onto the vector n.
rAC = vector C - vector A = (3 - 1)i + (1 - 0)j + (-1 + 1)k = 2i + j rAC × n = |rAC| cos θ = rAC × n / |n| = (2i + j) × ( -5i - 3j - 6k) / √(5² + 3² + 6²) = (-10 - 3 - 0) / √(5² + 3² + 6²) = \(\frac{-13}{\sqrt{70}}\)Therefore, the distance between the two skew lines is \(\frac{13}{\sqrt{70}}\).
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How many titles 250mm square will be needed to cover s kitchen floor of length 3m and breath 2.5m . The answer should be in the unit metre square
Answers
Answer:
30,000 tiles
Step-by-step explanation:
Area of tile = 250mm^2 = 0.25m^2
Total area of kitchen = 3*2.5 = 7.5m^2
No of tiles = 7.5/0.25 = 30,000 tiles
Find the inequality represented by the graph.
Answers
From the graph,
\(y = \frac{1}{2}x + 2\)
But this one is inequality so you gotta remember this:
When y > x/2+2
- The shade/region is above the graph itself.
When y < x/2+2
- The shade/region is below the graph.
Therefore, the inequality as shown in the picture is
\(y > \frac{1}{2} x + 2\)
Please no more cap answers, actually need help
Answers
Answer:
\(\sqrt{8x^{2} }\)+5-3 = 8.12
8.12 rounded to nears whole number is 8
therefore 8.12 rounded down to three decimal places is 8.1
Therefore your answer would be 8.1
If it wont let you add a decimal your answer would also be 8
Find f[g(x)] and g[f(x)] for the given functions. 3 f(x) = -x³ +3, g(x) = 4x+7 (Simplify your answer. Do not factor.) (Simplify your answer. Do not factor.) f[g(x)] = g[f(x)] =
Answers
The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19
The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7
The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below
f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3
When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343
Then
f[g(x)] = - 64x³ - 336x² - 588x - 340
Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;
g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g
[f(x)] = -4x³ + 19
Therefore,
f[g(x)] = - 64x³ - 336x² - 588x - 340
g[f(x)] = -4x³ + 19
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a highway superintendent states that four bridges into a city are used in the ratio 2334 durng the morning rush hour a highway study of an srs of 6000 cars indicates that
Answers
A highway superintendent states that four bridges into a city are used in the ratio 2:3:3:4 during the morning rush hour.
A highway study of an SRS of 6000 cars indicates that main answer in 40 words and explanation in 140 words.According to the question, there are four bridges into the city, and they are used in the ratio of 2:3:3:4.
That means that for every 2 cars coming from the first bridge, there are 3 cars coming from the second and the third bridges and 4 cars coming from the fourth bridge.According to the SRS of 6000 cars, the total number of cars from the first bridge is: 2/12 * 6000 = 1000
The total number of cars from the second bridge is: 3/12 * 6000 = 1500The total number of cars from the third bridge is: 3/12 * 6000 = 1500The total number of cars from the fourth bridge is: 4/12 * 6000 = 2000
Therefore, the number of cars coming from the first, second, third, and fourth bridges are 1000, 1500, 1500, and 2000, respectively, during the morning rush hour.
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