Answers
Answer:
[tex]\tan(30) = \frac{\sqrt 3}{3}[/tex]
[tex]\tan(60) = \sqrt 3[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find [tex]\tan(30)[/tex] and [tex]\tan(60)[/tex]
The tangent of an angle is calculated as:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
So, we have:
[tex]\tan(30) = \frac{b}{a}[/tex]
This gives:
[tex]\tan(30) = \frac{3}{3\sqrt 3}[/tex]
3 cancels out
[tex]\tan(30) = \frac{1}{\sqrt 3}[/tex]
Rationalize
[tex]\tan(30) = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}[/tex]
[tex]\tan(30) = \frac{\sqrt 3}{3}[/tex]
Similarly;
[tex]\tan(60) = \frac{a}{b}[/tex]
This gives:
[tex]\tan(60) = \frac{3\sqrt 3}{3}[/tex]
3 cancels out
[tex]\tan(60) = \sqrt 3[/tex]
Related Questions
I am voting in a state election. There are seven candidates for governor, four candidates for lieutenant governor, three candidates for the state house of representatives, and four candidates for the senate. In how many different ways can I fill out a ballot if I vote once for each office?
Answers
Answer:
4
Step-by-step explanation:
CHOOSE 1 GOVERNOR
CHOOSE 1 LIEUTENANT GOVERNOR
CHOOSE 1 STATE HOUSE REP'.
CHOOSE 1 SENATOR
=4 DIFFERENTNT WAYS.
Sade used the two blocks pictured to build a tower. What is the TOTAL VOLUME of the two blocks for this entire tower? *
Answers
Answer: V=120
have an amazing day <3
Answer:what is the answer i dont understand
plz help
HELPPP A GIRL OUT pleaseeee
Answers
Answer:
i think is b sorry if im wrong
Is the graph increasing , decreasing or constant
Answers
Answer: Constant.
The graph does not have an incline and therefore has a slope of 0. This means that the graph is constant.
RT and UW are parallel lines.
Which angles are corresponding angles?
Answers
Find the perimeter of triangle round nearest tength
Answers
This is the answer. I hope it helps!
(2a + 3b + 1) - (3a + 5b) - (2a - 2b – 3)
Answers
Answer:
4- 3a .............................
What is 1.63 to the third power
Answers
Answer: 4.330747
Step-by-step explanation: Hoped this helped:))
Answer:
4.330747
Step-by-step explanation:
1. Find
the area of each figure to the nearest tenth.
Answers
Area = 85ft²
To find the area of the given square you can use the following equation
[tex]Area = Side^2\\Area = 8^2\\Area = 64[/tex]
To find the missing side of the given triangle, you will have to use Pythagorean's theorem
[tex]Short^2 + Long^2 = Hypotenuse^2\\Short^2 + 8^2 = 10^2\\Short^2 + 64 = 100\\Short^2 = 100 - 64\\Short^2 = 36\\Short= \sqrt{36} \\Short= 6 \\[/tex]
Now that we know what both sides are we can use the following equation to get the area of the triangle
[tex]Area = \frac{Side*Side}{2} \\Area = \frac{6*8}{2} \\Area = \frac{42}{2} \\Area = 21 \\[/tex]
After that, we can add both areas together and get the following
[tex]21+64=85[/tex]
Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease.
Required:
a. If you wish to determine the community screening program has been effective, state the alternative hypothesis that should be tested.
b. State the null hypothesis.
c. If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using αα=.05 and explain the practical conclusion from your test.
d. Find the p-value for the test and interpret it.
Answers
Answer:
A) Alternative hypothesis; Ha: p_o > ⅔
B) Null hypothesis;
H0: p_o = ⅔
C) There is sufficient evidence to support the claim that the community screening programme was effective
D) p-value = 0
Its less than the significance value and so we will reject the null hypothesis and conclude that the community screening programme was effective
Step-by-step explanation:
A) We are told that ⅓ of those diagnosed eventually die of the disease. Thus, ⅔ is the fraction that will survive the disease.
Thus, the null hypothesis is;
H0: p_o = ⅔
We are told that a screening programme was started to increase the survival rate. Thus,the alternative hypothesis is;
Ha: p_o > ⅔
B) null hypothesis is;
H0: p_o = ⅔
C) 164 out of the 200 women selected survived the disease.
Thus sample proportion is;
p^ = 164/200
p^ = 0.82
For the z-score value, we will use the formula;
z = (p^ - p_o)/√((p_o(1 - p_o)/n)
Now, p_o = ⅔ = 0.67
Thus;
z = (0.82 - 0.67)/√((0.67(1 - 0.67)/200)
z = 4.51
From online p-value from z-score calculator, we have p-value ≈ 0
This is less than the significant level of 0.05 and therefore we will reject the null hypothesis and conclude that the community screening program was effective.
D) p-value ≈ 0
Reject the null hypothesis
which is the smallest integers, please answer, -9, 0, -2, -4, -11
Answers
Answer:
-11 :)
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
40 POINTS!!!!Which of the following is not a polynomial?
Answers
Answer:
5x²
Step-by-step explanation:
because polynomials are the expressions where many terms are involved
A shoe string is cut in to equal pieces that measure 0.50 of an inch. If the shoe string measures 7.50 inches, how many equal pieces can be cut?
Answers
Write the new points after the translation and write the rule in coordinate notation.
TRANSLATION: 1 unit left
Q
U
Q(2,-2), X(2,0), G(4,0), U(3,-4)
Answers
what is 7.09 Divided by 101
Answers
Answer:
0.070198..
Step-by-step explanation: its an on going number so make sure to put the line on top on the 0198
A teepee in the shape of a cone has a
radius of 7 feet and a height equal to
its diameter. What is the volume of the
teepee? Use 3.14 for .
Answers
The volume of the given cone is 718.01 square feet. Therefore, option H is the correct answer.
What is the volume of a cone?The volume of a cone is the amount of space occupied by a cone in a three-dimensional plane. A cone has a circular base, which means the base is made of a radius and diameter. The volume of a cone formula is 1/3 πr²h.
Given that, radius of a base of cone is 7 feet.
A height of a cone equal to its diameter = 7×2 = 14 feet
Here, volume of a cone = 1/3 ×3.14×7²×14
= 718.01 square feet
Therefore, option H is the correct answer.
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Describe the trend in the scatter plot . Explain your answer
Answers
From the given scatter plot it is a positive trend.
We need to describe the trend of given scatter plots.
How to identify the trend of the scatter plots?A scatter plot shows a positive trend if y tends to increase as x increases. A scatter plot shows a negative trend if y tends to decrease as x increases. A scatter plot shows no trend if there is no obvious pattern.
Here, from the given graph it is a positive trend.
Hence, from the given scatter plot it is a positive trend.
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Pls help I’ll brainlest ASAP
Answers
Answer:
B
Step-by-step explanation:
B is the best choice because the sample is random and represents a small portion of the entire school. The other choices are targeted for a specific group that wouldn't represent all students.
Answer:
B
Step-by-step explanation:
L
2.8
K
Solve AJKL. Round the answer to the nearest tenth.
A. J = 42.2°, K = 110.70, L = 27.1°
B. J = 110.70, K = 42.20, L = 27.1°
C. J = 42.2°, K = 27.1°, L = 110.70
D. J= 27.1°, K = 110.7°, L = 42.2°
Please select the best answer from the choices provided
Answers
Answer:
Result = 124.6
Step-by-step explanation:
If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit. Example
124.58
The first number of right of decimal point is 5
The second digit after decimal point is 8 which is greater than 5
So add 1 to 5
Result = 124.6
A and B are independent events P(A)=0.50 P(B)=0.30 What is P(A/B)
Answers
Answer:
0.50
Step-by-step explanation:
just did it
A researcher provides 10 children $100 each and another 10 children $20 each. She tracks how they decide to spend the money.
Which statement best describes the type of study the researcher is doing?
A. an observational study that is a statistical study
B. an observational study that is not a statistical study
C. an experimental study that is a statistical study
D. an experimental study that is not a statistical study
Answers
Answer:
C is the answer
Step-by-step explanation:
Its An experimental study that is a statistical study because it provides the researcher drawing back statistics from the children and its experimental because its based off of an experiment
Option C is correct, an experimental study that is a statistical study.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that a researcher provides 10 children $100 each and another 10 children $20 each. She tracks how they decide to spend the money.
We need to check the statement which best describes the type of study the researcher is doing.
An experimental study that is a statistical study because it provides the researcher drawing back statistics from the children and its experimental because its based off of an experiment
Hence, Option C is correct, an experimental study that is a statistical study.
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Find the distance between the pair of points (2,-1) and (-5,-5)?
Answers
Answer:
down 4 and over 7 so 11
Step-by-step explanation:
A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 167?
Answers
If a cone has a height of 16 feet and a volume
of 603.19 cubic feet, find the length of its
diameter.
Answers
Answer:
48 feet
Step-by-step explanation:
Use the equation: volume of a cone = 1/3 ×(height × radius ^2)
After finding the radius, multiply it with 2 to get the diameter
SOLVE
270.6 is 16 1/2% OF WHAT NUMBER?
WILL GIVE BRAINLIST
X
X
X
X
X
X
X
Answers
Answer:
approximately
1623.6
Step-by-step explanation:
16 1/2%=.165 which is approximately equal to 1/6, so we can just multiply the original number by 6.
Select all the equivalent ratios of 3:1
Answers:
A. 9:3 ; 6:2
B. 2:6 ; 3:9
C. 12:4 ; 15:5
D. 18:6 ; 27:9
Answers
Answer:
A,CStep-by-step explanation:
There are 64 teams in a basketball tournament. All teams play in the
first round but only winning teams move on to subsequent rounds.
Write an explicit rule for T(n), the number of games in the nth round of
the tournament. State the domain:
Answers
The domain of this function is n ≥ 1, where n is the round of the tournament.
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
The explicit rule for T(n), the number of games in the nth round of the tournament is 2ⁿ⁻¹. The domain of this function is n ≥ 1, where n is the round of the tournament.
Since all teams play in the first round, the number of games in the first round (n = 1) is 2¹⁻¹, which is equal to 1. As the rounds progress, the number of games in each round is doubled. T
herefore, the number of games in the second round (n = 2) is 2²⁻¹, which is equal to 2. The number of games in the third round (n = 3) is 2³⁻¹, which is equal to 4.
This pattern continues for each round, as the number of games in the nth round is 2ⁿ⁻¹.
Therefore, the domain of this function is n ≥ 1, where n is the round of the tournament.
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If
you had 2 angles that equal 180 degrees and you was given a angle of
55 degrees What degree is the missing angle? *
Answers
Answer:
125 degrees for 540 degrees total
Step-by-step explanation:
Answer:
125° is the missing angle.
Step-by-step explanation:
Sum of all angles in a quadrilateral is 360°.
180°+55°+X°= 360°
235° + x = 360°
x = 360°-235°= 125°
x = 125°
A furniture manufacturing company manufactures dining-room tables and chairs. A table requires 8 labor-hour s for assembling and 2 labor-h ours for finishing. A chair requires 2 labor-hours for assembling and 1 labor-hour for finishing. The maximum labor-hours available p er day for assembly and finishing are 400 and 120, respectively. If x is the number of tables and y is the number of chairs produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y.
Required:
Find the set of feasible solutions graphically for the number of tables and chairs that can be produced.
Answers
Answer:
See Annex In blue feasible region ( using Geogebra)
Step-by-step explanation:
Table 1.-
Assembling hours finishing hours
Product (tables) x 8 2
Product ( chairs) y 2 1
Availability 400 120
Constrains:
1.-Availability of assembling hours 400
8*x + 2* y ≤ 400
2.-Availability of Finishing hours
2*x + 1*y ≤ 120
3.-General constraints
x ≥ 0 y ≥ 0 integers
$10,000 is invested at 0.75% annual interest for 2 years.
a. Simple Interest b. Compound Interest
Answers
Answer:
The simple interest is 10,150.00 The compound interest is $10,150.56
Step-by-step explanation: