Answers
The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13
How to solve Trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
From the given image, we see that;
Hypotenuse = 13
Adjacent = 12
Opposite = 5
Thus;
tan θ = 5/12
θ = tan⁻¹(5/12)
sin θ = 5/13
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Related Questions
(b) The amount of pure acid in 40 oz of 15% acid solution is
(Type an integer or a decimal.)
OZ.
Answers
Using the percentage, the amount of pure acid in 40 oz of 15% acid solution is 6 OZ.
In the given question,
The amount of pure acid in 40 oz of 15% acid solution is in OZ.
As we know that percentage is represent as a ratio of 100. So we solve it by converting the percentage.
So
=40×15%
So the simplified form is
=40×15/100
Simplifying
=6
Hence, the amount of pure acid in 40 oz of 15% acid solution is 6 OZ.
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based on information from a large insurance company, 68% of all damage liability claims are made by single people under the age of 25. a random sample of 52 claims showed that 41 were made by single people under the age of 25. does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company? give the test statistic and your conclusion.
Answers
Yes, it indicates that the number of single people under the age of 25 is higher than the national percentage reported by the large insurance company, according to the calculated z-score.
here the sample size is = 25(n), therefore sample proportion will be, p⁰= 41/25 =0.774 .since the null hypothesis is :H₀:p =0.68 and the alternative hypothesis is :H₁:p>0.68 .The z-test is :
Z=p⁰−p/ √(p(1-p)/n
= 0.774-0.68/root(0.68(1-0.68)/52
=1.453
The p-value for the z score = 1.453 is 0.0731.Here the P-value is greater than the 5% level of significance. We come up short to dismiss the null hypothesis at the 5% level of significance. it can be concluded that the number of single individuals under the age of 25 is higher than the national percentage detailed by the large insurance company.
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Ayúdame de método de eliminación 3x3
5× - 3y - z =1
× + 4y - 6z = -1
2× + 3y + 4z =9
Answers
The solution to the system of equations, using elimination, is given as follows:
x = 0.0135, y = -0.2767, z = -0.1024.
How to obtain the solution to the system of equations?The solution to the system of equations is obtained using the elimination method, as the variables are written as functions of each other and then solved.
The system in this problem is composed by the equations presented as follows:
5x - 3y - z = 1.x + 4y - 6z = -1.2x + 3y + 4z = 9.From the first equation, the variable z is written as function of variables x and y, as follows:
z = 5x - 3y - 1.
Replacing in the second equation, we have that:
x + 4y - 6(5x - 3y - 1) = -1
-29x + 22y = -7.
Replacing in the third equation, we have that:
2x + 3y + 4(5x - 3y - 1) = -1
22x - 9y = 3.
Hence the system is now:
-29x + 22y = -7.22x - 9y = 3.Multiplying the first equation by 9 and the second by 22, we have that:
-261x + 198y = -63.484x - 198y = 66.Adding the equations, the solution for x is obtained as follows:
223x = 3
x = 3/223
x = 0.0135.
Then the solution for y is obtained as follows:
-261(0.0315) + 198y = -63
y = (-63 + 261(0.0315))/198
y = -0.2767.
The solution for z is:
z = 5(0.0135) - 3(-0.2767) - 1 = -0.1024,
TranslationThe problem asks to solve the system of equations using the elimination method.
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Polynomial as the product of linear factors
Answers
The polynomial, f(x) expressed as a product of linear factors is; f(x) =(-5/2 + √ 5) and (-5/2 - √ 5)
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Given that ;
[tex]p(A) = 2x^3 - 3x^2 + 10x + 6[/tex]
[tex]P(a)= (2x^3 - 3x^2) + (10x + 6)[/tex]
therefore need to further factorise the quadratic expression (x² + 5x +3) using the quadratic formula;
Quadratic formula;
x = {-b ± √(b² +4ac)}/2a
where; a = 1, b = 5, c = 3.
Therefore; x = -5/2 + √ 5or x = -5/2 - √ 5
Therefore, the other factors are:
(-5/2 + √ 5) and (-5/2 - √ 5)
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The finding, publihed recently in the journal Cell Sytem, calculate that a 5-year-old dog would be puhing 60 in human year. What i the percent change from the old model' to the new model' etimation of a 5-year-old dog' age? Round your anwer to 2 place after the decimal
Answers
The percent change from the old model to the new model estimation of a 5-year old dog's age is 41.66% .
The traditional model involved multiplying the dog's age with seven to calculate their age in human years. for example if the age of dog is 3 years , so in human years he/she will be 3x7 = 21 years old in human years.
Here we calculate the age of 5-years old dog in human years. So we multiply the 5 with 7 and get the answer as 35 years .
As per the new convention 5-years old dos's age is nearly equal to 60 in human years.
So the difference in age in both the methods is
age difference = 60 - 35
= 25
So the percent change in age = (25/60) x 100
= 41.66 %
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The senior classes at high school A and high school B planned separate trips to the county fail. The senior class at high school A rented and filled 7 vans and 12 busses with 640 student. High school B rented and filled 12 vans and 6 busses with 456 students. Each van and each bus carried the same number of students. Find the number of students in each van and each bus.
Answers
7v + 12b = 640
12v + 6b = 456
Multiply the bottom equation by -2 in order to cancel out 12b with 6b.
7v + 12b = 640
- 24v -12b = -912
-17v = -272
17v = 272
v = 272/17
v = 16 students
If we use this: 7v + 12b = 640 ;then:
7(16) +12b = 640
112 +12b = 640
12b = 640 -112
12b = 528
b = 528/12
b = 44 students
So the number of students in each van is 16, and number of students in each bus is 44.
Quiz Grade
100
98
95
92
88
85
80
75
Frequency
:=Z=Z_
||
What is the
range of
the quiz
grades?
Answers
Answer:
Step-by-step explanation:
1. Find definition of range: the difference between the highest and lowest values.
Highest value:100
Lowest Value 75
2. Caculate:
100-75=
25 is the range
Answer: 25 is range
Answer:
range is 25.
ffd
Step-by-step explanation:
.... yyyy
Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x+8)² - 1
lesser x =
greater x =
Answers
The zeroes of the polynomial is -7,-9 and the lesser x = -9, greater x = -7.
What is zeroes of polynomial?
We already know that a polynomial is an algebraic term with one or many terms. Zeroes of Polynomial are the real values of the variable for which the value of the polynomial becomes zero. So, real numbers, ‘m’ and ‘n’ are zeroes of polynomial p (x), if p (m) = 0 and p (n) = 0.
Given
f(x) = (x+8)² - 1
=x^2+64+16x-1
=x^2+16x+63
=x^2+7x+9x+63
=x(x+7)+9(x+7)
=(x+7)(x+9)
therefore, x=-7,-9
The lesser x = -9,
the greater x = -7.
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9. (6.NS.1) A model train is 15 3/4 inches long. Each car in this train is 2 5/8 inches in length. How many cars are in the train?
Answers
Answer:
3 cars
Step-by-step explanation:
We know this because 15 3/4 is the same as 63in and 3 5/8 is the same as 21. So we divide 63÷21=3
an anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. the results were as follows:837 drank alcohol regularly, 639 smoked cigarettes, 176 used illegal drugs, 388 drank alcohol regularly and smoked cigarettes, 100 drank alcohol regularly and used illegal drugs, 105 smoked cigarettes and used illegal drugs, 83 engaged in all three behaviors, and 358 engaged in none of these behaviors. a) how many students were surveyed? of those surveyed, b) how many drank alcohol or smoked cigarettes ? c) how many drank alcohol only? d) how many drank alcohol and smoked cigarettes , but did not use illegal drugs ? e) how many smoked cigarettes or used illegal drugs , but did not drink alcohol ? f) how many engaged in exactly two of these behaviors? g) how many engaged in at least one of these behaviors?
Answers
a) Total surveyed students=1500
b) Drank alcohol or smoked cigarettes=1088.
c) Drank alcohol only=432
What is Venn Diagram?
A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects. They frequently serve to visually group objects while highlighting how they differ and how they are similar.
Given, Alcohol drank → 857
Smoked cigarettes → 639
Illegal drugs used → 176
Drank alcohol regularly and smoked cigarettes → 388
Drank alcohol regularly and used illegal drugs →100
Smoked cigarettes and used illegal drugs → 105
Engaged in all three behaviors → 83
Engaged for none of these → 358
Notation used, Alcohol (A), Drugs (D), Cigarettes (C)
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5.15 Find what percent one number is of another: word problems 498
After a month of successful fundraising, David and his classmates voted on whether to donate
the money they had raised to hunger relief or to environmental causes. Out of 27 votes, 27
were for hunger relief. What percentage of the votes were for hunger relief
Write your answer using a percent sign (%).
Submit
Answers
Answer:
100%
Step-by-step explanation:
If all 27 votes for hunger relief, that would be 100% or all of them.
6/19.08 _
.
_ help plsssssssssssssssssssssssssssssssssssssssssssss
Answers
Answer:
0.3144654088
Step-by-step explanation:
6/19.08=0.3144654088
A parabola can be drawn given a focus of (-4,-3) and a directrix of y = 1. Write the equation of the parabola in any form?
Answers
Answer:
Step-by-step explanation:
To plot
(
−
4
,
−
3
)
, start at the origin
(
0
,
0
)
and move left
4
units and down
3
units.
(
−
4
,
−
3
)
Prove algebraically that
(4n+ 1)²- (2n-1) is an even number
for all positive integer values of n.
Answers
(4n+1)^2 = 16n^2 + 8n + 1
(16n^2 + 8n + 1) - (2n - 1) = 16n^2 + 6n + 2
this means that it must always be an even number because the positive integer n is multiplied by an even number. and then it is added by 2, which will keep it even. should be right
can someone please help me?
Answers
Answer:
b i think
Step-by-step explanation:
becuase 45f in total and for every hour it decreses 2f the anwser would be b but i may be wrong
What are the domain and range of the function on the
graph?
The domain includes all integers, and the range is y 2
0.
The domain includes all integers, and the range is y >
0.
The domain includes all real numbers, and the range
is y ≥ 0.
The domain includes all real numbers, and the range
is y > 0.
Answers
The domain includes all real numbers, and the range is y > 0
What are domain and range?
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range. In general, a function's domain and range are denoted as follows: Range(f) = f(x): x domain(f) and domain(f) = f(x): x R
Domain: The domain is the set of all possible x-values.
Range: The range of a function is the complete set of all possible resulting values of the dependent variable y.
We can see from the graph, x values include all real numbers and range ( y values greater than 0 because the graph line does not intersect at 0.
we know that
The domain of the function of the graph is the interval (-∞,∞)
That means the domain is all real numbers.
The range of the function of the graph is the interval is (0,∞)
That means the domain is all real numbers greater than zero.
So, Option d is correct.
Therefore,
The domain includes all real numbers, and the range is y > 0.
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I need this answer if anyone can help please do.
Thank you!
Answers
Answer:
u should ask a teacher
Step-by-step explanation:
they wouldn't get mad but happy asked
I HOPE THIS HELPED!!!
Lance threw a die six times. His median score was 3.5. His first five throws were 1,5,3,5,1. What was his sixth throw?
Answers
Answer: Sixth throw is 6
Step-by-step explanation: Let sixth throw be 'x'
1+5+3+5+1+x/6=3.5
15+x=3.5*6
15+x=21
x=6
Answer:3
Step-by-step explanation: literally just subtract 2 each time its not hard
2-1+5x4x11 I need help with this
Answers
Answer:
221
Step-by-step explanation:Order of operations
hanna properties specializes in custom-home resales in an exclusive subdivision of phoenix, arizona. a random sample of nine custom homes currently listed for sale is provided in the following table, in size (hundreds of square feet) and price of the home (thousands of dollars):the data is shown in the following table: square feet 26 27 33 29 29 34 30 40 22 price 259 274 294 296 325 380 457 523 215 if you wanted to predict the sales price based upon square footage for homes in this subdivision, what would be the slope of the least squares regression line? a. approx 15.89 b. approx -140.00 c. approx 0.68 d. none of the above
Answers
To determine what satisfying assumptions 1-3 would mean by considering the variable under consideration.
The regression-inference Assumptions 1-3 must be satisfied if β°, β¹ and σ are constants, which ensures the x dimensions and price of every custom home to be normal, with β° + β¹ and a σ standard deviation.
The residuals should not be linear if the normal probability plot is followed.
In the diagram above, the assumptions for regression inferences appear to be unsatisfactory.
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Please help (Algebra 1)
Answers
The y-intercept in the equation is 10. This is the initial height of the flower.
What is the y-intercept?
An exponential equation can be described as an equation with exponents. The exponent is usually a variable. When an exponential function is drawn on a coordinate graph, it is usually nonlinear because the slope is not constant.
The general form of exponential equation is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe y-intercept of an exponential function is the value of y when x is zero. It is the point where the graph intersects the y-axis. The y-intercept represents the initial height of the flower.
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A toy company makes bags of 134 action figures. Each bag can vary
by 2 action figures.
Write an absolute value linear inequality that represents the range of
the acceptable amount of action figures in every bag. Use x as your
variable.
Answers
Answer:
x= 134 ± 2
Step-by-step explanation:
The ± symbol is used to mark the range of values that should be expected from the first number, 134.
help please..............................
Answers
Answer:
With what?
Step-by-step explanation:
Answer:
Step-by-step explanation:
d
If transcription progresses at the rate of 40 nucleotides per second, how long it would take to transcribe a sequence that is 3. 6 x 104 bases long?.
Answers
20 to 25 minutes Transcription occurs at a rate of 40 nucleotides per second.
Given,
In the question:
If transcription progresses at the rate of 40 nucleotides per second.
To find the how long it would take to transcribe a sequence that is 3. 6 x 104 bases long?
Why is a nucleotide necessary?
Nucleotides have a variety of roles in animal physiology, including those of energy storage, transporters of activated metabolites for biosynthesis, structural moieties of coenzymes, and metabolic regulators.
Give an example of nucleotides and describe them.
A nucleotide is the fundamental part of nucleic acids (RNA and DNA). A nucleotide is made up of a nitrogen-containing base, a phosphate group, and a sugar molecule (either ribose in RNA or deoxyribose in DNA). The nucleotides used in DNA are adenine (A), cytosine (C), guanine (G), and thymine (T).
Hence, 20 to 25 minutes Transcription occurs at a rate of 40 nucleotides per second.
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show that, if the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated.
Answers
If the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated as a wait operation atomically decrements the value associated with a semaphore.
Semaphores refers to integer variables utilized to solve the critical section problem by using two atomic operations, wait and signal that are used for process synchronization. The wait operation decreases the value of its argument S, if it is positive and if S is negative zero or negative, then no operation occurs. The signal operation increases the value of its argument S. Operation wait() and signal() must be completely atomic or else it violates the mutual exclusion. Mutual exclusion refers to the property of process synchronization which asserts that “no two processes can exist in the critical section at any given point of time”.
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a particle moves in a vertical plane along the closed path seen in (figure 1) starting at aa and eventually returning to its starting point. figure1 of 1 part a is the work done by gravity positive, negative, or zero? explain.
Answers
In the given situation, the work done by gravity is zero as any work done during a downward part of the motion as undone during the upward parts.
Work refers to the measurement of energy transfer that happens when an object is moved over a distance by an external force which is applied in the direction of the displacement. Hence, the work done is given by the multiplication of force and displacement in the direction of force i.e., W = F x d. As in the given case, the displacement d = 0 as the particle returns to the same point. The work done by gravity would measure the displacement along the y-axis and as the total displacement is zero, hence, work done will be zero.
Note: The question is missing the figure which is attached.
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what is -13/10 x 6 in mixed fractions?
Answers
The fraction -(13/10) × 6 is equal to the mixed fraction -7 whole number 4 divided by 5.
How to change improper fraction to mixed fractionFrom the given fracion;
-(13/10) × 6 = -[13/(2×5)] ×2 × 3
we divide the common factor 2 for 10 and 6
-(13/10) × 6 = -(13/5) × 3
multiply the numerators
-(13/10) × 6 = (-13×3)/5
-(13/10) × 6 = -39/5
divide -39 by 5
-(13/10) × 6 = -7 whole number, 4/5 in mixed fraction
Therefore, the mixed fraction for -(13/10) × 6 is -7 4/5.
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an unbiased coin is tossed 20 times. 6. find the probability that the coin lands heads exactly 11 times. a. 0.1602 b. 0.5731 c. 0.2941 d. 0.1527 e. 0.6374 7. find the probability that the coin lands tails at most 17 times. a. 0.0002 b. 0.8748 c. 0.7812 d. 0.0176 e. 0.9998 8. find the probability that the coin lands heads at most 3 times. a. 0.0004 b. 0.9963 c. 0.9556 d. 0.8751 e. 0.0013
Answers
Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.
Given:
an unbiased coin is tossed 20 times.
The probability that the coin lands heads exactly 11 times:
P = n(E)/n(S)
n(S) = 2^tosses
= 2^20
= 1048576
n(E) = C(20,11)
= 20!/11!(20-11)!
= 20!/11!*9!
= 167960
Probability P = 167960/1048576
= 0.16017 ≈ 0.1602
Therefore Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.
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Point x has the coordinates (4,1). You translate it using the rule (x+3, y-5). What are the coordinates of X'?
Answers
Answer: X'=
(7,-4)
Step-by-step explanation: We have the rule (x+3,y-5) so using the given coordinates (4, 1), we can find the answer by doing this => (4+3,1-5)=(7,-4)
The average cost to a 50-year-old male for a $100,000 term life policy is $14. 34 per month. The same policy would cost a 70-year-old male $79. 79 per month. How much more will the 70-year-old pay for a 20-year term?.
Answers
70-year-olds pay an extra $15708 for a 20-year term.
Given;
The average cost to a 50-year-old male for a $100,000 term life policy is $14. 34 per month. The same policy would cost a 70-year-old male $79. 79 per month.
A 70-year-average old's monthly expense (MAC) is $79.79
A 50-year-average old's monthly expense (MAC) is $14.34
MAC → Monthly Average Cost
To get how much more will the 70-year-old pay for a 20-year term;
We will multiply the monthly value by the yearly and solve the given data,
The extra amount paid = (MAC of 70 years old * 12 - MAC of 50 years old * 12) * 20 years term.
= ($79.79 * 12 - $14.34 * 12) * 20
= ($957.48 - $172.08) * 20
= $15708
Hence, the excess amount 70-year-old pay for a 20-year term is $15708.
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