1) The length of AC is 14.
2) The length of AB is 8.
3) The length of BC is 17.
4) The length of AB is 29.1.
5) The length of BC 53.
6) The measure m∠C is 53.8°
What is sine rule of a triangle?
AB/sin C = BC/ sin A = AC / sin B
1)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
22° + 118° + ∠C = 180°
∠C = 40°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 24, ∠C = 40°, and ∠B = 22°:
AB/sinC=AC/sin B
24/sin 40° = AC/ sin 22°
AC = 13.98
AC ≈ 14
2)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 7, ∠B = 44°, and ∠C = 53°:
AC/sin B=AB/sin C
7/sin 44° = AB/ sin 53°
AB = 8.047
AC ≈ 8
3)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
39° + ∠B + 51°= 180°
∠B = 90°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 27, ∠B = 90°, and ∠A = 39°:
BC/sinA=AC/sin B
BC/sin 39° = 27/ sin 90°
BC = 16.99
BC ≈ 17
4)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
∠A + 101° + 63°= 180°
∠A = 16°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting CB = 9, ∠A = 16°, and ∠C = 63°:
AB/sinC=BC/sinA
AB/sin 63° = 9/ sin 16°
AB = 29.09
AB ≈ 29.1
5)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
93° + ∠B + 58° = 180°
∠B = 29°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 16, ∠B = 29°, and ∠A = 93°:
AC/sinB=BC/sin A
16/sin 29° = BC/ sin 93°
BC = 32.95
BC ≈ 33
6)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 21, ∠A = 88°, and BC= 26:
AB/sinC=BC/sinA
21/sin C = 26/ sin 88°
sin C/21 = sin 88°/26
C = 53.82
C ≈ 53.8
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In statistical process control, when a point falls outside of control limits, the probability is quite high that the process is experiencing _____________ .
A. common cause variation
B. student t variation
C. a reduction of variables
D. special cause variation
When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.
In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.
On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.
When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.
Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.
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price level (p) value of money (1/p) quantity of money demanded (billions of dollars) 1.00 1.5 1.33 2.0 2.00 3.5 4.00 7.0
The relationship between price level (P), value of money (1/P), and quantity of money demanded (Q) is as follows:
As P increases, the value of money (1/P) decreases.
As P increases, the quantity of money demanded (Q) increases.
In macroeconomics, the quantity theory of money is a concept that states that the supply and demand for money determine the level of prices.
The concept is based on the assumption that the velocity of money (the rate at which money is exchanged in the economy) and real output are constant.
This theory is expressed mathematically as follows: MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is real output.
The relationship between the price level, value of money, and quantity of money demanded can be explained through the quantity theory of money equation: MV = PQ
Where M is the money supply, V is the velocity of money, P is the price level, and Q is the quantity of goods and services produced in an economy.
We can rearrange this equation to solve for P:
P = MV/Q
Now, using the given data, we can find the relationship between price level (P), value of money (1/P), and quantity of money demanded (Q):
Price Level (P)Value of Money (1/P)
Quantity of Money Demanded (billions of dollars)1.001.5001.3312.003.504.007.0
To calculate the value of money (1/P), we need to take the reciprocal of each value of P. For example, if P = 1, then 1/P = 1/1 = 1.
Using the formula P = MV/Q, we can calculate the value of M by rearranging the equation: M = PQ/V. Since we don't have data for V, we can assume that it is constant (i.e., V = 1).
Therefore, M = PQ.To calculate the quantity of money demanded (Q), we can use the formula Q = MV/P. Again, assuming that V is constant at 1, we get Q = M/P.So, using the data in the table, we can calculate:
M = PQ = 1.00 x 1.5 = 1.5Q = MV/P = 1.5 x 1.00 = 1.5 billion dollars
M = PQ = 1.33 x 2.00 = 2.66Q = MV/P = 2.66 x 1.33 = 3.54 billion dollars
M = PQ = 2.00 x 3.50 = 7.00Q = MV/P = 7.00 x 2.00 = 14.00 billion dollars
M = PQ = 4.00 x 7.00 = 28.00Q = MV/P = 28.00 x 4.00 = 112.00 billion dollars
Therefore, the relationship between price level (P), value of money (1/P), and quantity of money demanded (Q) is as follows:
As P increases, the value of money (1/P) decreases.
As P increases, the quantity of money demanded (Q) increases.
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The answer to the quantity of money demanded (billions of dollars) is shown in the table below.
Price level (p)Value of money (1/p)Quantity of money demanded (billions of dollars)1.001.55.001.333.52.007.04.0012.5
As per the table given above, the quantity of money demanded (billions of dollars) is as follows for the respective price level (p) given below:
When the price level is 1.00, the quantity of money demanded is $5 billion.
When the price level is 2.00, the quantity of money demanded is $3.5 billion.
When the price level is 4.00, the quantity of money demanded is $12.5 billion.
The table provided above shows the relationship between the price level and the quantity of money demanded.
It can be observed that as the price level increases, the value of money decreases and the quantity of money demanded increases.
This shows an inverse relationship between the value of money and the quantity of money demanded.
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a student government organization is selling christmas trees as a fundraiser. on friday, they sold noble fir trees and douglas fir trees for a total of . on saturday, noble fir trees and douglas fir trees were sold for a total of . what is the cost per tree for each type?
In linear equation, the noble is $ 120 and the douglas is $200 are the cost per tree for each type.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.n= noble fir trees
d= douglas fir trees
5n + 3d = $420
12n + 9d = $1,080
multiply the second equation by 3
36n + 18d = 3,240
now divide the equation by 18
2n + d = 180
-2n -2n
d = 180 - 2n
Now put that equation in the first as d
5n + 3(180 -2n) = 420
5n + 540- 6n = 420
- 540 -540
1n = 120
n = 120
Now put n into the second equation( none changed one) to find d
12(120) + 9d = 3240
1440 + 9d = 3240
-1440 -1440
9d = 1800
÷9 ÷9
d= 200
so the noble is $ 120
and the douglas is $200
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The complete question is -
A student government organization is selling Christmas trees as a fundraiser. On Friday, they sold 5 noble fir trees and 3 douglas fir trees for a total of $420. On Saturday, 12 noble fir trees and 9 douglas fir trees were sold for a total of $1,080. What is the cost per tree for each type?
If k(x) = 2x^2 - 3√x then k(9) is. ?
PLEASE HELP
k(9) = 2(9)^2 - 3√9
= 2(81) - 27
= 162 - 27
= 135
If k(x) = 2x^2 - 3√x then k(9) is equal to 2(9)^2 - 3√9 which simplifies to 2(81) - 27 = 162 - 27 = 135 1
Simplify 3x + (2+7x)
Answer:
10x+2
Step-by-step explanation:
3x+(2+7x)=3x+2+7x
=10x+2
Do you know the code to the lock on the refrigerator? enter it without any spaces.
the specific lock code for your refrigerator. However, I hope this explanation helps you understand the concept of lock codes and their purpose in securing devices and objects.
but I cannot provide the code to the lock on your refrigerator. As an AI helper on Brainly, I don't have access to specific lock codes for individual appliances.
However, if you are trying to understand the concept of lock codes, I can provide a general explanation. A lock code is a combination of numbers, letters, or symbols that is used to secure and restrict access to a device or object, such as a refrigerator. It acts as a password or key to prevent unauthorized individuals from opening the lock.
The lock code for a refrigerator is typically set by the owner or manufacturer and can be personalized for security purposes. It is important to keep the lock code confidential to ensure that only authorized individuals can access the refrigerator.
I cannot provide the specific lock code for your refrigerator. However, I hope this explanation helps you understand the concept of lock codes and their purpose in securing devices and objects.
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alice and bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for alice. if they play 6 rounds, in how many ways can alice win or draw exactly three times? (answer: 300)
AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240
Permutation:
In probability, permutation refers the arrangement of objects in a definite order.
Given,
Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.
Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.
While we looking into the given question, we know that,
Total number of games = 6
Possible values = 3 ( win, loss, or draw)
Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,
=> 6! / (6 - 3)!
=> 6! / 3!
=> 120
Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,
=> 6!/ (6 - 3)!
=> 120
So, the number of ways can Alice win or draw exactly three times is
=> 120 + 120 = 240
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A rock is 7 feet below the surface of a river. If its position can be recorded as -7, what would the position of 0 represent?
A. On the surface of the river
B. At the bottom of the river
C. 7 feet above the surface of the river
D. 7 feet below the surface of the river
4.2...PLZZZZ I HAVE A 60 IN MATH HELP ME
Answer:
1:3
Step-by-step explanation:
It’s ratios.
A: 3
B: 9
36
129
C: x3
solve for x. pls help
Answer:
Step-by-step explanation:
5)50=x+59 => x=-9
6)x+77=70 => x=-7
7)x+123=115 => x=-8
8)11x-1=10x+10 +> x=11
9)120+5x+10=180 => 5x=50 =>x=10
10)125=x+134 => x=9
The picture below will help you to understand this question better.
A machine can wrap 360 packages of muffins in 12 minutes. At this rate, how
many packages will be wrapped in 1 hour?*
Answer:
1800 (packages )muffins
Step-by-step explanation:
360 muffins x muffins
-------- = --------
12 min 60 min
Answer:
1800 maybe
Step-by-step explanation:
in 12 minutes can wrap 360
in 1 hr have 60 minutes
60/12=5
than 360*5 = 1800
Molly is selling candy bars for a fundraiser. She started at 12:00p.m.with 60 bars and ended at 5:00p.m. with 20. How many bars did Molly sell per hour?
Answer:
she sold 15 candy bars every hour
Step-by-step explanation:
Simplify the expression:
3+9+2k–2
Answer:
2k+10
Step-by-step explanation:
Good luck!
10. A manufacturer makes conical funnels for
professional painters. The funnels are
formed from plastic with a 9-inch
diameter base and a height of 9 inches.
After the cones cool, a machine cuts off
1 inch of the tip to leave a 1-inch
diameter hole in the end. What is the
volume of the funnel? Show your work.
Answer:
The volume of the cone after the tip is cut off equals 150 cubic inches
Step-by-step explanation:
The dimensions of the cone formed from the funnel are given as height equals 9 inches and, radius equals 4 inches (radius = 8/2).
The volume of a cone is determined as follows;
Volume = πr²h/3
Volume = π x 4² x (9/3)
Volume = π x 16 x 3
Volume = 48π
When a portion of the cone is cut off from the tip, the height from the cut off part is 1 inch and the radius is 0.5 inch (radius = 1/2).
The volume of the cut off portion can now be calculated as;
Volume = πr²h/3
Volume = π x 0.5² x (3/3)
Volume = π x 0.25 x 1
Volume = 0.25π
Hence the volume of the cone after the tip has been cut off is now derived as follows;
Volume = 48π - 0.25π
Volume = 47.75π
Volume = 47.75 x 3.14
Volume = 149.935
Volume ≈ 150 cubic inches (Rounded to the nearest whole number)
I hope this helps :)
H(x)=-5/6x;h(x)=10
Find the value of x so that the function has the given value
The value of x = -12.
Define Function.
A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")
The given expression is
H(x)=-5/6 x
also, H(x) = 10
so, put H(x) value in given expression,
10 = -5/6 x
Now, solve for 'x'
-5x = 60
x = 60/(-5)
x = -12
Therefore, the value of x = -12
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Part B
A new machine with better technology produces 210 gel pens every fifteen minutes. What is the constant of proportionality in the relationship between the number of gel pens and the number of minutes
The constant of proportionality i
Proportionality constant of p is = 14 t
WHAT IS PROPORTIONALITY CONSTANT ?The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.
CALCULATIONy = kx
The rate k = 210 ÷ 15 = 14 gel pens per minute
"p" is number of pens, "t" is number of minutes
p = 14t
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The seventh-grade class at Van Buren Middle School spent $225.98 on supplies for a car wash. The day of the car wash it rained and they only earned $82.75. What were the net earnings of the car wash?
Net earnings mean the total of.
-225.98 + 82.75 is saying that they spent 225.98 on supplies and made 82.75
-143.23 is the result you get:
adding &subtracting negative numbers
5 + (-3) - 6=?
Answer:
-4
Step-by-step explanation:
5+(-3)-6=
5-3-6=
= -4
to divide data with a high value of h and a low value of l into k classes, the class interval must be:
The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.
The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.
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What is the solution to n/4 = -12.4?
n = 3.1
n = -3.1
n = 49.6
n = -49.6
Answer:
n= -49.6
Step-by-step explanation:
49.6 i did this test and got it right
12/18/2020
Scale Drawings
Question #6
Amanda made a scale drawing of a square garden, which has a side length of 25 feet. She used the scale
2 inches = 5 feet.
What will be the area of the scale drawing?
Answer:
,twenty five divided by five
A ream of paper contains 500 sheets, and a case of paper contains 10 reams. An office supply store gets a delivery of 400 cases. How many sheets of paper are in the delivery? Express your answer in scientific notation.
Answer:
2,000,000 or 2x10^6
Step-by-step explanation: Multiply the total number of sheets in a ream times the total number of reams in a case times the number of cases.
what are odds of winning mega millions
The odds of winning the Mega Millions jackpot are approximately 1 in 302 million.
The chances of winning the Mega Millions Jackpot, which requires matching each of the five white balls and the gold Super Ball, are around 1 of every 302 million. The chances of winning any award in Uber Millions, which incorporates matching essentially the Super Ball, are around 1 of every 24. The size of the award relies upon the quantity of matching numbers and the Super Ball, with the big stake being the biggest award. The likelihood of winning the bonanza increments somewhat as the quantity of tickets sold increments, however it stays an exceptionally low likelihood occasion. Notwithstanding the slim chances, a great many individuals play the Uber Millions lottery consistently with expectations of becoming quite wealthy.
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Shawna is making smoothies. The recipe
calls for 2 parts yogurt to 3 parts
blueberries. Shawna wants to make 10 cups of smoothie mix. How many cups of
yogurt and blueberries does Shawna need?
What decimal is equivalent to 6.38%?
Answer:
6.38 as a decimal is 0.0638 and you can multiply 0.0638 by a number to 6.38 percent of that number
Answer:
0.0638
Step-by-step explanation:
Percent means 'per 100'. So, 6.38% means 6.38 per 100 or simply 6.38/100.
If you divide 6.38 by 100, you'll get 0.0638 (a decimal number).
As you can see, to convert from percent to decimal just divide the percent value (6.38) by 100, and remove the "%" sign.
PART G: Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?
Part H
Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.
Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.
Part J
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given two angles and the side between them.
Under Sides, enter 5 for a. Under Angles, enter 30 for B and 50 for C. Then click Calculate. How many triangles can be created from the given conditions?
Part K
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given three sides of specified length.
Under Sides, enter 6 for a, 7 for b, and 13 for c. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given side lengths.
please help!
The solutions are given below.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Part A
the dotted line formes the thrid side of the triangle.
part B
The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.
part c
If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.
part D
You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.
part e
The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.
part f
Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters
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A certain town has two kinds of youth basketball teams. One is a school team (S) and the other is a rec team (R). On any given Saturday in December, the probability that a school team will have a game is 0.8, and the probability that a rec team will have a game is 0.7. The probability that both have games us 0.65.
On any given Saturday in December, what is the probability that either a rec team or a school team has a game?
Answer Choices:
0.65
0.7
0.8
0.85
Answer:
D. 0.85
Step-by-step explanation:
Given
Probability of S = 0.8
Probability of R = 0.7
Probability of S and R = 0.65
Required
Probability of S or R
Using probability notations;
P(S) = 0.8
P(R) = 0.7
P(S n R) = 0.65
The question requires that we solve for P(S or R)
For overlapping events S and R; the following formula is applicable.
P(S or R) = P(S) + P(R) - P(S n R)
Substitute the values of P(S), P(R) and P(S n R)
P(S or R) = 0.8 + 0.7 - 0.65
P(S or R) = 0.85
Hence, the probability that either a rec team or a school team has a game is 0.85
I need help please help
Answer:
:) good day mate
Step-by-step explanation:
:) indeed
He signed a promissory note with a term of three years the principal was $12,800 with interest at 12.5% how much did BP pay in interest on the note and on the maturity date how much did bo4 principal
Answer:
$48,000
Step-by-step explanation:
Step one:
given data
Principal= $12,800
rate= 12.5%
time = 3 years
Required
The Interest
Step two
SImple interest= PRT/100
substitute
SI= 12800*12.5*3/100
SI=480000/100
SI=$48,000
Find the length of the third side. If necessary, write in simplest radical form.
The length of the third side is 4.
Given information:
A right-angled triangle is provided in the diagram.
So, as per the diagram,
The hypotenuse leg = √(97)
Opposite leg = 9
Let the length of the adjacent leg, which is the third side be x. By the Pythagorean theorem, we have:
x² + 9² = √(97)²
Simplifying the right side, we get:
x² + 81 = 97
Subtracting 81 from both sides, we get:
x² = 16
Apply square root property, we get,
x = +/- 4
Since the length of a side of a triangle must be positive, the length of the third side is 4.
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