I need help quickly, I'm preparing for a test! Help is appreciated!
Solve each triangle. Round your answers to the nearest tenth. (#4)
Answers
The measure of angle ∠A and angle ∠C will be 65.37° and 17.63°. And the measure of the length of CA will be 29.48 inches.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
In triangle ABC, the side AB is 9 in, the side BC is 27 in, and the angle B is 97 degrees.
Then the other two angles and the side CA will be
The side CA is given by the cosine rule. Then we have
\(\rm CA^2 = AB ^2+ BC^2 - 2 \times AB \times BC \cos B\\\\\\CA^2 = 9^2 + 27^2 - 2 \times 9 \times 27 \cos 97^o\\\\\\CA^2 = 810 + 59.23\\\\\\CA ^2 = 869.23\\\\\\CA \ = 29.48 \ in\)
Then angle A will be given by the sine rule. Then we have
\(\dfrac{27}{\sin A} = \dfrac{29.48}{\sin 97^0}\\\\\\\sin A = \dfrac{27 \sin 97^0}{29.48}\\\\\\\sin A = 0.9090\\\\\\A \ \ \ \ = 65.37^0\)
Then the angle C will be
∠A + ∠B + ∠C = 180°
65.37° + 97° + ∠C = 180°
∠C = 17.63°
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Related Questions
help me please , for 20 points
Answers
Answer:
A
Step-by-step explanation:
First off we can see that there are 46 pencils - and 7 students - so we can divide the two
46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.
If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.
Now that we know that each student gets 6 pencils, we need to find out how many are left.
We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.
only question 3 A and B please thank you
Answers
Answer:
smell my feet nnnnnnnnnsdsdsdnnnsdsdnigdsga
Step-by-step explanation:
a soccer team has 13 players. a starting lineup consist of 11 players, one of whom is a goalkeeper and the other 10 regular players (players are interchangeable). how many different starting lineups can the team have?
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The soccer team can have 1,716 different starting lineups. The number of ways to choose 1 player out of 13 for the goalkeeper position is given by the combination formula: C(13, 1) = 13.
To calculate the number of different starting lineups, we need to determine the combinations of players that can be chosen for the starting lineup. Since there are 13 players on the team and 11 positions in the starting lineup, we need to choose 1 player for the goalkeeper position and 10 players for the regular positions. Similarly, the number of ways to choose 10 players out of the remaining 12 players for the regular positions is given by the combination formula:
C(12, 10) = 66.
To find the total number of different starting lineups, we multiply the number of choices for the goalkeeper position by the number of choices for the regular positions: 13 * 66 = 858.
However, the order of the players in the lineup doesn't matter, so we need to divide the result by the number of permutations of the 10 regular players: 858 / 10! = 1716. The soccer team can have 1,716 different starting lineups.
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When one increases the confidence level (1-α), say from 0.90 to 0.95, what happens to the width of the confidence interval? a. It stays the same b. It becomes wider c. It becomes narrower
Answers
Step-by-step explanation:
A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.
a philosophy professor assigns letter grades on a test according to the following scheme. a: top 13% of scores b: scores below the top 13% and above the bottom 62% c: scores below the top 38% and above the bottom 15% d: scores below the top 85% and above the bottom 8% f: bottom 8% of scores scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5 . find the minimum score required for an a grade. round your answer to the nearest whole number, if necessary.
Answers
To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.
Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:
x = μ + (z * σ)
where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:
x = 69.5 + (1.04 * 9.5) ≈ 79.58
Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.
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An independent set in a graph is a set of vertices S⊆V that contains no edge (so no pair of neighboring vertices is included). The max independent set problem is to find an independent set of maximum size in a graph G. (a) Write the max independent set problem as an integer linear program. (b) Write an LP relaxation for the max independent set problem. (c) Construct an example (a family of graphs) to show that the ratio LP-OPT / OPT can be at least cn where c>0 is some absolute constant and n is the number of vertices of the graph. (d) What is the (exact) relation between the size of a max independent set and the size of min vertex cover of a graph? (e) Using this relation, what does the 2-approximation algorithm for vertex cover imply for an approximation algorithm for max independent set?
Answers
The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.
The solution for this question is discussed below:
a) The integer linear program for the max independent set problem is as follows:
maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.
b) The LP relaxation for the max independent set problem is as follows:
Maximize ∑x_iSubject to:
xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.
c) The family of graphs is as follows:
Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.
d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.
e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.
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plssss help. I have no idea how to do it its due today
Answers
Answer: X=23
<u is 75
< v is 29
<w is 76
Step-by-step explanation:
< u + < v +< w = 180
<w + 3x+35 = 180
so 3x+35= <v+ <u
3x+35=x+52+x+6
3x+35= 2x+58
x+35=58
x= 23
so each angle
U= (23+52)= 75
V= (23+6)= 29
W=180-75-29= 76
or 3(23)+35+w=180
104+w=180
w= 76
What is the sum of the interior angles of the polygon shown below?
Answers
Answer:
360
Step-by-step explanation:
Formula
Sides -2 ×180
4-2=2×180=360
express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 3 π , 5 π ]
Answers
The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].
To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.
The given sum can be written as:
lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],
where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].
To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:
lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,
where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.
Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].
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a radio station gives a pair of concert tickets to the th correct caller who knows the birthday of the performer. for each person who calls, the probability is of knowing the performer's birthday. all calls are independent. define to be the number of calls needed to find a winner. (a) is a random variable. that is, identify the type of random variable and its parameter(s). (b) what is the probability that the th caller wins the tickets? (c) what is the probability that the station will need or more calls to find a winner?
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The likelihood that the station will need 13 or more calls to determine a winner is 0.5 because each call is independent.
What is independent?Events A and B are considered to be independent events if their likelihood of occurring does not change as a result of the possibility that A will occur. P(A) = P(AB) = 1/2, which suggests that the likelihood of event. A occurring has not changed as a result of event B's happening. A pair of occurrences is considered independent if the occurrence of one does not change the likelihood that the other will also occur. The likelihood of both A and B happening is equal to the product of the probabilities of A and B (i.e., P), which is how mathematics expresses the independence of events A and B. (A and B)To learn more about independent, refer to:
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m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.
The figure shows straight angle P Q R that consists of two smaller angles, P Q S and R Q S.
34
41
21
56
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The value of x is 41 . Option B
How to determine the angleIt is important to note that angles on a straight line are known to be supplementary.
Supplementary angles are defined as angles that sum up to 180 degrees.
From the information given, we have that;
m∠PQS=(3x−3)° m∠RQS=(x+19)Since angles on a straight line sum up to 180 degrees, we have that;
m∠PQS + m∠RQS = 180°
Substitute the values into the equation
3x - 3 + x + 19 = 180°
collect like terms
4x = 180 - 16
4x = 164
Make 'x' the subject of formula
x = 164/4
x = 41
Thus, the value of x is 41 . Option B
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Jack purchases 4 pounds of colby jack cheese if the price is $ 5.98 per pound how much did jack pay
Answers
Answer:
$28.92
Step-by-step explanation:
4 x 5.98
Answer:
23.92
Step-by-step explanation:
5.98 (4) = 23.92
what would be the rate of change
Answers
The rate of change of the table is $0.8 per pencil
How to determine the rate of changeFrom the question, we have the following parameters that can be used in our computation:
The table of values
Using the above as a guide, we have the following:
Rate of change = Cost/Pencils
Substitute the known values in the above equation, so, we have the following representation
Rate of change = 6.4/8
Evaluate
Rate of change = 0.8
Hence, the Rate of change is $0.8
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what is the nth term rule of the linear sequence below 15, 7, -1, -9, -17
Answers
Answer:
8n+7
Step-by-step explanation:
An item is regularly priced at %59 . It is on sale for 35% off the regular price. what is the sales price
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Answer: 38.35%
Step-by-step explanation:
59%=59/100=0.59
0.59-0.35(0.59)=
0.59-0.2065=
0.5900-0.2065=
0.3835=38.35%
Find the value of y
for the given value of x
.
y=3x+2;x=0.5
Answers
Answer:
3.5
Step-by-step explanation:
y = 3x+2
= 3(0.5) + 2
= 1.5+2
= 3.5
As part of statistics project, math class weighed all the children who were willing to participate as shown below.
How many children weighed less than 50 pounds?
Answers
Answer:
18
Step-by-step explanation:
The key of this leaf stem-leaf plot is:
4 | 5 = 45
Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:
First row => 12, 13, 15, 15 15, 16, 16, 19
Second row => 23, 25
Third row => 33, 35, 37, 38, 39
Fourth row => 44, 45, 45
Therefore, the number of children that weigh less than 50 pounds = 18
consider the function. f(x) = sin(x), 0 < x < find the half-range cosine expansion of the given function.
Answers
The half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to f(x) = (2/π).
To find the half-range cosine expansion of the function f(x) = sin(x) for 0 < x < π, we can utilize the half-range Fourier series expansion. The half-range expansion represents the function as a sum of cosine terms.
The half-range Fourier series expansion of f(x) can be expressed as:
f(x) = a₀/2 + ∑[n=1 to ∞] (aₙ * cos(nx))
To find the coefficients a₀ and aₙ, we can use the following formulas:
a₀ = (2/π) ∫[0 to π] f(x) dx
aₙ = (2/π) ∫[0 to π] f(x) * cos(nx) dx
Let's calculate the coefficients:
a₀ = (2/π) ∫[0 to π] sin(x) dx
= (2/π) [-cos(x)] [0 to π]
= (2/π) [-cos(π) + cos(0)]
= (2/π) [1 + 1]
= 4/π
For aₙ, we have:
aₙ = (2/π) ∫[0 to π] sin(x) * cos(nx) dx
= 0 [since the integrand is an odd function integrated over a symmetric interval]
Now, we can rewrite the half-range cosine expansion of f(x):
f(x) = (4/π) * (1/2) + ∑[n=1 to ∞] (0 * cos(nx))
= (2/π) + 0
Therefore, the half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to:
f(x) = (2/π)
In this expansion, all the cosine terms have coefficients of zero, and the function is represented solely by the constant term (2/π).
It's worth noting that the half-range cosine expansion is valid for the given interval (0 < x < π), and outside this interval, the function would need to be extended or expressed differently.
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Pls help me it’s due tonight
Answers
Answer:
slope: 1/4
x-intercept: (-20,0)
y-intercept: (0,5)
Step-by-step explanation:
hope that helps
an insurance company has called a consulting firm lo determine if the weather an unusually high number of false insurance claims have been filed. it is known that the industry proportion for false claims is 3%. the consulting firm has randomly and independently chosen a sample of 100 of the insurance claims. they believe the number of these 100 that are false will yield the information the company desires. what type of distribution should the consulting company choose to represent the occurrence of false claims?
Answers
Answer:
I dont really understand can you explain it better Step-by-step explanation:
2. Tamika is on page 20 of her book and reads 4 pages every night. Mark is on page 30 of the same book
and reads 2 pages every night. How long will it take Tamika to be further in the book than Mark?
Answers
Answer:
7 nights
Step-by-step explanation:
Tamika: Mark:
20 30
24 32
28 34
32 36
36 38
40 40
44 42
48
52
56
60
Is pi divided by 7 rational or irrational?
I WILL GIVE BRAINIEST PLEASE HELP!!
Answers
Answer:
rational
Step-by-step explanation:
\(\pi + 28\)
what is Pi + 28
Answers
What is the perimeter of rectangle CDEF?
Answers
Answer: its sixty-nine
Step-by-step explanation:its my lucky number
how do i solve 2.5a+12=5a
Answers
Answer:
a
=
4.8
Step-by-step explanation:
there
2.5a+12=5a
subtract 12 from both sides
2.5a=5a-12
subtract 5a from both sides
-2.5a=-12
divide both sides by -2.5
a=4.8
The circumference of the inner circle is 44 ft.
The distance between the inner circle and the outer circle is 4 ft.
Answers
Answer:176 is the answer if your asking for the outer circles circumfer
Step-by-step explanation:
what is 4 1/2 as a percent
Answers
Answer:
450%
Step-by-step explanation:
4 1/2
1/2 = 50%
4=400%
400%+50%=450%
450%
Answer
450%
Step-by-step explanation: 4.5 × 100% = 450%
Use the properties of radicals to simplify the expression
Answers
The properties of radicals to simplify the expression is 2 √22. .
What characteristics does a radical expression have?Using Radical PropertiesAn expression that contains a radical is referred to as a radical expression. When all three requirements are satisfied, an expression containing a radical with index n is expressed in its simplest form. No radicands other than one have perfect nth powers as factors. There are no fractions in radicands.The product property of radicals and the quotient property of radicals are obtained by combining these two things. These two characteristics demonstrate that the square root of a product is equal to the sum of its component square roots. The denominator of a fraction has no radicals.\(\sqrt[3]{6} * \sqrt[3 ]{72} / \sqrt[3]{2}\) =2 √22.
2 √22 = 88 .
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Factor:9/100 x^2 - 4/25
Answers
Answer:
\(\frac{9}{100}x^2-\frac{4}{25}=(\frac{3}{10}x-\frac{2}{5})(\frac{3}{10}x+\frac{2}{5})\)Explanation:
Given the expression:
\(\frac{9}{100}x^2-\frac{4}{25}\)This can be written as a difference of two squares. But before that, we can rewrite the expression as:
\((\frac{3}{10}x)^2-(\frac{2}{5})^2\)So, as a different of two squares, we write:
\((\frac{3}{10}x-\frac{2}{5})(\frac{3}{10}x+\frac{2}{5})\)cylindrical container of paint is 3 cm across the top and about 7 cm high. how many cubic centimeters of paint can it hold?
Answers
The number of cubic centimeters of paint that will fit in the cylindrical container is:
66.36 cm³
How to find the volume of a cylindrical container?The volume of a cylinder can be determined by multiplying the area of the base by the height. It may be expressed using the formula:
V = πr²h
where π (pi) is approximately equal to 3.14, r is the radius, and h is the height.
You should also note that the radius of the cylinder is one-half of the diameter.
V = πr²h
Since the cylindrical container of paint has a diameter of 3 cm, its radius would be 1.5 cm. Furthermore, its height is around 7 cm. As a result, by substituting the given values into the formula, we may get the following result:
V = πr²hV = π(1.5)²(7)
V = 66.36 cm³
Therefore, the cylindrical container of paint can hold approximately 66.36 cubic centimeters of paint.
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