Solve the triangle. The Law of Cosines may be needed. (Standard notation for triangle ABC is used throughout. Use a calculator and give your answers as decimals to tenth at the end of the computation. If no such triangle exists, enter 'NONE' in each of the answer blanks.)
b = 31.9, c = 14.7, C = 27.8°
Answers
Answer:
Step-by-step explanation:
To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees.
Given:
b = 31.9
c = 14.7
C = 27.8°
To find angle A, we can use the Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
We know b, c, and C, so we can substitute the values:
a^2 = 31.9^2 + 14.7^2 - 2 * 31.9 * 14.7 * cos(27.8°)
Now, we can solve for a:
a = sqrt(31.9^2 + 14.7^2 - 2 * 31.9 * 14.7 * cos(27.8°))
To find angle B, we can use the Law of Sines:
sin(B)/b = sin(A)/a
We know b and a, so we can substitute the values:
sin(B)/31.9 = sin(A)/a
Now, we can solve for sin(B):
sin(B) = (sin(A)/a) * 31.9
Finally, we can solve for angle B:
B = arcsin((sin(A)/a) * 31.9)
To find angle C, we can subtract angles A and B from 180°:
C = 180° - A - B
Now, we can calculate the values:
A = acos((b^2 + c^2 - a^2) / (2 * b * c))
B = arcsin((sin(A)/a) * 31.9)
C = 180° - A - B
Using the given values, we can calculate the triangle:
A ≈ acos((31.9^2 + 14.7^2 - a^2) / (2 * 31.9 * 14.7))
B ≈ arcsin((sin(A)/a) * 31.9)
C ≈ 180° - A - B
Please note that the final numerical calculation is required to provide the exact values for A, B, and C.
Related Questions
Mr. Correa’s financial planner says his net worth is $94,520.00. Using the table, below determine which of the following statements is true.
Answers
Answer:
Yes, because the sum of his assets is $125,480 and the sum of his liabilities is $20,960.
Step-by-step explanation:
60 percent of the employees of a company are women and 75% of the women earn 20000 or more in a month. Total number of employees who earns more than 20000 per month in the company is 60 percent of the total employees. What fraction of men earns less than 20000 per month
Answers
Let's assume there are 100 employees in the company.
Given information:
60% of the employees are women, which means there are 60 women in the company.
75% of the women earn 20000 or more, which means 75% of 60, i.e., 45 women earn 20000 or more.
The total number of employees who earn more than 20000 per month is 60% of the total employees, which means 60% of 100, i.e., 60 employees earn more than 20000.
Now, let's find the number of men in the company. Since the total number of employees is 100 and 60 of them are women, the remaining 100 - 60 = 40 employees must be men.
To calculate the fraction of men who earn less than 20000 per month, we need to find the number of men who earn less than 20000. We can subtract the number of men who earn more than 20000 from the total number of men.
Total men = 40
Men who earn more than 20000 = 60 - 45 = 15
Men who earn less than 20000 = Total men - Men who earn more than 20000
= 40 - 15
= 25
Therefore, the fraction of men who earn less than 20000 per month is 25/40, which simplifies to 5/8.
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what is the lowest base in which the number 1000 could be a valid number?
Answers
The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.
In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.
Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:
1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0
where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.
We can see that if we set base = 2, then the equation becomes:
1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0
Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.
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Last Friday, Kira and Marcy got dinner at seaside sushi restaurant. Kira ordered 2 prices of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Kira and Marcy order the ratio of tuna and crab?
Pls help me
Answers
Answer: \(\frac{5}{11}\)
Step-by-step explanation:
Given
Kira order 2 pieces of tuna and 5 pieces of crab
While Marcy ordered 3 pieces of tuna and 6 pieces of crab
Total tuna ordered =2+3=5 pieces
Total crab ordered=5+6=11 pieces
The ratio of Tuna and crab is \(\frac{2+3}{5+6}=\frac{5}{11}\)
Using the solution from the previous question, solve the following problem. Suppose that the amount of money originally invested in an account was $5,000, and that the money in the account after 3 years is $6,050. What was the annual simple interest rate for the account?
Answers
Let's use the simple interest formula:
\(FV=PV\cdot r\cdot t\)Where:
FV = Future value = $6050
PV = Present value = $5000
r = interest rate
t = time = 3
Replacing the data into the equation:
\(\begin{gathered} 6050=5000\cdot r\cdot3 \\ 6050=15000r \\ \text{Solving for r:} \\ \frac{6050}{15000}=r \\ \\ r\approx0.4033\approx40.33 \end{gathered}\)r = 40.33%
y -25 = 89
y - 25 + ___ = 89 +25
y = ____
Answers
y - 25 + 25 = 89 + 25
y - 25 + 25 = 114
y = 114
what is 45x32 please help me
i need help asap
Answers
Answer:
1440
Step-by-step explanation:
Answer:
1440 is the answer to 32 x 45
if 15 out of the 200 patients admitted to a hospital remain longer than a week, how many of the 2800 admissions in a given year were relaeased within one week
Answers
Answer:
15 × 14 = 210 of the 2,800 admitted patients remained longer than a week, so 2,800 - 210 = 2,590 of those patients were released within one week.
Find the distance between A (4. - 1) and B (-3,0)
Answers
Answer:
hope this is correct
(Chapter 12) If u * v = 0 and u X v = 0, then u or v = 0
Answers
Therefore, in either partial derivatives, we have u = 0 or v = 0.
The given information implies that two vectors u and v satisfy:
u * v = 0, where * denotes the dot product between vectors.
u X v = 0, where X denotes the cross product between vectors.
From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.
From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:
|u X v| = |u| * |v| * sin(θ)
= 0
Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).
In the case where u and v are parallel, we have:
u * v = |u| * |v| * cos(θ)
= |u|²
= 0
This implies that |u| = 0, which means that u = 0.
In the case where u and v are anti-parallel, we have:
u * v = |u| * |v| * cos(θ)
= -|u|²
= 0
This again implies that |u| = 0, which means that u = 0.
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Find the length of arc AB when the diameter of circle C is 10 inches.
20π in
2600π in
125π9 in
25π9 in
Answers
Answer:
Its the third one
Step-by-step explanation:
i did the test
Suppose you are holding stock and there are three possible outcomes. The good state happens with 20% probability and 18% return. The neutral state happens with 55% probability and 9% return. The bad state happens with 25% probability and −5% return. What is the expected return? Please enter the answer as a percent with two decimal places for instance 55.55 for 55.55% Suppose you are holding a stock and there are three possible outcomes. The good state happens with 20% probability and 18% return. The neutral state happens with 55% probability and 9% return. The bad state happens with 25% probability and −5% return. What is the standard deviation of return? Please enter a number (not a percentage). Please convert all percentages to numbers before calculating, then type in the number. Now type in 4 decimal places. The answer will be small. Suppose you are holding a stock and there are three possible outcomes. The good state happens with 20% probability and 18% return. The neutral state happens with 55% probability and 9% return. The bad state happens with 25% probability and −5% return. What is the variance of return? Please enter a number (not a percentage). Please convert all percentages to numbers before calculating, then type in the number. Now type in 4 decimal places. The answer will be small.
Answers
The standard deviation of returns is 0.0665 when a person is holding stock and there are three possible outcomes.
To calculate the expected return, we multiply the probability of each state by its corresponding return and sum them up:
Expected return = (20% * 18%) + (55% * 9%) + (25% * -5%)
Expected return = 0.20 * 0.18 + 0.55 * 0.09 + 0.25 * (-0.05)
Expected return = 0.036 + 0.0495 - 0.0125
Expected return = 0.073
The expected return is 7.30%.
To calculate the standard deviation of returns, we need to find the variance first. The variance is calculated as the weighted sum of squared deviations from the expected return:
Variance = (20% * (18% - 7.30%)^2) + (55% * (9% - 7.30%)^2) + (25% * (-5% - 7.30%)^2)
Variance = 0.20 * (0.1077)^2 + 0.55 * (0.0177)^2 + 0.25 * (-0.123)^2
Variance = 0.00232 + 0.000173 + 0.001903
Variance = 0.004423
The standard deviation is the square root of the variance:
Standard deviation = √(0.004423)
Standard deviation = 0.0665
Therefore, the value obtained is 0.0665.
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Es el valor de la incógnita en la siguiente igualdad: x/Sen30°= 8/Sen45°
Answers
Respuesta:
x = 5.656854249
Explicación paso a paso:
[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]
x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]
x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]
x = 5.656854249
Calculate the surface area of this cylinder. Use 3.14 for the value of pi.
Answers
Answer:
1884.96 cm squared
The phrase "correlation does not mean causation" is often thrown around. What does it mean? Is it accurate? Why or not? I'm looking for your personal interpretation and analysis. (6 points) Use the editor to format your answer
Answers
"Correlation does not imply causation; a statistical association does not prove a cause-and-effect relationship."
Why is the phrase "correlation does not mean causation" often mentioned?Correlation refers to the statistical association between two variables, indicating that they tend to change together. However, this does not imply that one variable directly causes the other. It is crucial to recognize that correlation can arise due to various factors, including coincidence, third variables, or complex interactions.
Correlation is a valuable tool in research, as it helps identify patterns and relationships. However, inferring causation from correlation requires additional evidence and rigorous investigation. Observational studies, where variables are simply observed, often face limitations in establishing causality. Controlled experiments or randomized controlled trials are preferred in establishing causation as they involve manipulating variables and controlling for confounding factors.
In the field of science, it is essential to distinguish between correlation and causation. Researchers must be cautious when drawing conclusions based solely on observed associations. Relying solely on correlation can lead to misleading interpretations and incorrect assumptions about causality.
To establish causal relationships, researchers employ various methods such as controlled experiments, longitudinal studies, or meta-analyses, which provide stronger evidence for causation. By understanding the limitations of correlation and conducting rigorous research, scientists can unravel complex relationships and contribute to accurate knowledge and informed decision-making.
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What is an equation of the line that passes through the points (5, 5) and (5, -8)
Answers
Answer:
Write the problem as a mathematical expression. (5,5), (5,−8)
Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept. To calculate the equation of the line, use the y=mx+b format.
Slope is equal to the change in y over the change in x , or rise over run.
m=(change in y)/(change in x)
The change in x is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
m=(y2−y1) / (x2−x1)
Substitute in the values of x and y
into the equation to find the slope.
m=(−8−(5)) / (5−(5))
Finding the slope m.
Undefined
x=5
Step-by-step explanation:
Answer:
m = undefined
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (5, 5)
Point (5, -8)
Step 2: Identify
(5, 5) → x₁ = 5, y₁ = 5
(5, -8) → x₂ = 5, y₂ = -8
Step 3: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: \(\displaystyle m=\frac{-8-5}{5-5}\)[Slope] Subtract: \(\displaystyle m=\frac{-13}{0}\)Here we see that we have a number divided by 0. Since we know that we cannot divide any number by 0, our slope will be undefined. This will be a vertical line on a Cartesian plane of x = 5.
use the venn diagram to identify the population and the sample
Answers
The Venn diagram can be used to visually represent the population and the sample, allowing for a clear identification of both entities within a given context.
A Venn diagram is a graphical representation that uses overlapping circles to illustrate the relationships between different sets. It can be helpful in identifying the population and the sample in a given context. In a Venn diagram, the population refers to the entire set or group being studied. It represents the complete collection of individuals or elements that the researcher wants to draw conclusions about. The population is typically represented by the universal set encompassing all the circles in the Venn diagram.
On the other hand, a sample is a subset or a smaller portion of the population that is selected for observation or data collection. It represents a representative portion of the population and is often used to make inferences or draw conclusions about the larger population. In the Venn diagram, the sample would be represented by the specific area or overlap between the circles that corresponds to the selected subset of the population. It is important to note that the sample is derived from the population and should ideally be representative of it to ensure the validity of any conclusions drawn.
By utilizing the Venn diagram, researchers can visually distinguish the population from the sample, aiding in understanding the relationships and subsets within the given study context.
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Identify a positive coterminal angle for the angle shown below. You must answer in radians.
Answers
Express 5.5 recurring as mixed number
Answers
Answer:
5.5 = 5 5/10 = 5 1/2 (simplified)
Hope this helps in any way :)
Annie round $280. 05$ to the nearet hundred. Bobby round $280. 05$ to the nearet ten. Ciro round $280. 05$ to the nearet integer. Denie round $280. 05$ to the nearet tenth. What i the um of Annie' anwer, Bobby' anwer, Ciro' anwer, and Denie' anwer?
Answers
The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.
What is rounding off the numbers?A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.
If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.
Annie rounds $ 280.05 to the nearest hundred
$ 280.05 will be equal to $ 300
Bobby rounds $ 280.05 to the nearest ten
$ 280.05 will be equal to = $ 280
Ciro rounds $ 280.05 to the nearest integer
$ 280.05 will be equal to = $ 280
Denise rounds $ 280.05 to the nearest tenth
$ 280.05 will be equal to = $ 280.1
Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280 + $ 280.1 = $ 1140.1
Therefore,
The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.
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It cost Angel $6.75 to send 75 text messages. How much does it cost to send one text?
Answers
Answer:
$0.09 or nine cents!
Step-by-step explanation:
Divide 6.75 by 75
Answer:0.09 cents
Step-by-step explanation:
because if you trying find cost per text you divide 6.75/75 =0.09.
what value of x will make the sides equal
3x+94 = 21+94
Answers
Answer:
7
Step-by-step explanation:
because 3x7 =21
☺️☺️☺️☺️☺️
Answer:
x=7
Step-by-step explanation:
Subtract 94 from both sides and you get
3x=21
Then divide both sides by 3
21 divided by 3 is equal to 7
The answer is 7
Hope that helps :)
A line passes through the points (7, 10) and (7,20). Which statement is true about the line?
12-1
It has a slope of zero because X2 - X, in the formula m-
Xq-X,
is zero, and the numerator of a fraction cannot be
zero.
Y2-11
It has a slope of zero because Xz - X, in the formula m-
X₂ - X,
is zero, and the denominator of a fraction cannot be
zero.
Y2-11
It has no slope because X2 - X, in the formula -
X2-X,
is zero, and the numerator of a fraction cannot be zero.
It has no slope because X2 – X, in the formula m
12-11
X2 - X,
is zero, and the denominator of a fraction cannot be zero,
Answers
Answer:The answer is It has no slope because x2 - x1 in the formula m=y2-y1-x2-x1 is zero, and the denominator of a fraction cannot be zero
Step-by-step explanation:
I did the quiz
Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.
Answers
Answer:
x = 12
Step-by-step explanation:
sqrt(x+4) - 3 = 1
First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.
sqrt(x+4) = 1 + 3
sqrt(x+4) = 4
To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.
(sqrt(x+4))^2 = 4^2
x + 4 = 16
subtract 4 to finish up.
x = 12
Check:
sqrt(12 + 4) - 3 = 1
sqrt16 - 3 = 1
4 - 3 = 1
1 = 1 Check!
how to represent -23/6 on number line
Answers
So -23/6 = -3 5/6
Make a number line with (on the left) -4, -3, -2 -1 , 0 , 1, 2, 3, 4
Then put a dot very close to -4 BUT not on -4
Reaching out 2 standard errors on either side of the sample proportion makes us about _________ confident that the true proportion is capable within the interval
a. 90%
b. 99%
c. 95%
d. 68%
Answers
The correct answer is option c. 95%. Reaching out two standard errors on either side of the sample proportion gives us an interval of 95% confidence.
This is due to the fact that two standard errors on either side of the sample proportion will cover around 95% of the population's cases.
We can typically determine the true proportion in the population using this range of two standard errors on either side of the sample proportion.
This is because it helps us identify any potential outliers in the population and provides a range of population proportions for which we may be 95% certain.
We are 95% certain that the true percentage is capable inside the interval if we stretch out two standard errors on either side of the sample proportion.
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pls give explanation and steps ik it equals zero
f(5)=-(5)^3+7(5)^2-7(5)-15
Answers
Answer:
0 (as you already know)
Step-by-step explanation:
First we will simplify both sides of this equation:
5f = -125 + 175 + -35 + -15
Now we are going to Combine Like Terms:
5f = (-125 + 175 + -35 + -15)
5f = 0
Divide both sides by 5
5f / 5 = 0 / 5
F = 0
Hope this helps
Favorite days of the week Monday 55% Tuesday 45% 4) If 220 people were surveyed, how many more people voted for Monday than for Tuesday?
Answers
Answer: 22
Step-by-step explanation:
Ok, so the way I do it I multiply then divide.
For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday
For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.
So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)
How to solve 2.43 * 13 in a algorithm.
Answers
Answer:
31.59
Step-by-step explanation:
Attached below!
(Btw: I dont know wht algorithm is but i tink its wht i just did.... so hope its right! )
JUST MULPLY ITS EASY DZUHH
an ice sculture measures 52 inches and melts continuously by 3% per minute. find the height of a sculpture after 15 minutes
Answers
Answer:
28.6 inches
Step-by-step explanation:
3 percent of 52 is 1.56 so it is melting at a rate of 1.56 inches per minute
15x1.56 is 23.4
52-23.4=28.6 so after 15 minutes the sculpture will be only 28.6 inches tall