Answers
1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.
How to answer the aforementioned question1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.
tan θ = 5/12 = sin θ / cos θ
Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.
Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:
[tex]cos^2[/tex] θ = 1 - sin^2 θ
[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]
[tex]cos^2[/tex]θ = 1 - 25/144
[tex]cos^2[/tex] θ = 119/144
cos θ = √(119/144)
cos θ = √119/12
Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:
[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ
[tex]sin^2[/tex]θ = 1 - (119/144)
[tex]sin^2[/tex]θ = 25/144
sin θ = √(25/144)
sin θ = 5/12
Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:
sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6
Therefore, sin θ + tan θ is equal to 5/6.
2) The value of sin θ is already calculated as 5/12.
3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.
Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:
sec θ = 1/cos θ = 1/(√119/12) = 12/√119
csc θ is the reciprocal of sin θ, so:
csc θ = 1/sin θ = 1/(5/12) = 12/5
Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:
sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25
4) To find cot θ + sin θ, we need to calculate the value of cot θ.
cot θ is the reciprocal of tan θ, so:
cot θ = 1/tan θ = 1/(5/12) = 12/5
Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:
cot θ + sin θ = 12/5 + 5/12
To add these fractions, we need a common denominator:
cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)
= 144/60 + 25/60
= 169/60
Therefore, cot θ + sin θ is equal to 169/60.
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Related Questions
Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Answers
Answer:
8 2/5
Step-by-step explanation:
42/5
to find the improper fraction, divide the numerator by the denominator
and then find the remainder
42 / 5 = 8 ( 5*8) the remainder is 42-40 = 2
Put the remainder over the denominator
8 2/5
Hey there!
Question reads….
Which mixed number is equivalent to the improper fraction 42/5?
EQUATION:
42/5
The one that is equivalent to the fraction is:
8 2/5
Reason:
8 2/5
= 8 * 5 + 2 / 5
= 40 + 2 / 5
= 42 / 5
Therefore, your answer should be:
Option C. 8 2/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which of the following is true about horizontal asymptotes?
a.) A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ .
b.) All horizontal asymptotes describe what happens when x gets close to 0 .
c.) All rational functions have at least one horizontal asymptote.
d.) All horizontal asymptotes describe what happens when the denominator's value gets close to 0.
Answers
A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
What are horizontal asymptotes?A horizontal asymptote of a graph can be defined as a horizontal line at y = b where the graph tend to approach the line as an inputs approach to infinity ( ∞ or –∞).
A slant asymptote of a graph is known as a slanted line y = mx + b where the graph approaches the line as the inputs approach the positive infinity ∞ or to the infinity –∞.
Thus, a function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
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Good recordkeeping helps protect assets and helps managers?
Answers
Answer:
yes i help yes of course he help
483,800,000 place value of 4
Answers
Answer:
hundred million is the place value of 4 in 483800000
A committee of 6 members is to be selected from 8 senior and 10 junior. find how many ways can this be done if there is no restriction
Answers
Answer:
18564 ways
Step-by-step explanation:
The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :
then
This can be done in [tex]C^{6}_{18}[/tex] ways.
[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]
Chris bought a new car for 12,500 he made 3,000 down payment and financed the rest for 14.5% for 36 months for 3 years how much less would his total be for same loan 24 months 2 years
Answers
The difference in total loan repayments between the two mortgage payment option is 771.12
The requirement here is to determine the difference between total loan repayments when the period of loan is 36 months and the total repayments when the period of loan is 24 months instead.
Note the loan amount is the excess of purchase price over the down payment required.
loan amount=12,500-3,000
loan amount=9,500
The monthly payment in each case can be determined using the present value formula of an ordinary annuity.
PV=monthly payment*(1-(1+r)^-N/r
36-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=36
9,500=X*(1-(1+0.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-0.6489543809903260)/0.0120833333333333
9,500=X*0.3510456190096740/0.0120833333333333
9,500=X*29.0520512283869000
X=9,500/29.0520512283869000
X=327.00
Total month repayments=327.00*36
Total month repayments=11,772.00
24-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=24
9,500=X*(1-(1+0.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-0.7495652524008220/0.0120833333333333
9,500=X*0.2504347475991780/0.0120833333333333
9,500=X*20.7256342840700000
X=9,500/20.7256342840700000
X=458.37
Total month repayments=458.37*24
Total month repayments=11,000.88
Difference in total payments=11,772.00-11,000.88
Difference in total payments=771.12
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Answer:
just 771.21
Step-by-step explanation:
to make it shorter credits to the og person who said the awnser 771.21
tephen uses \dfrac{2}{25}
25
2
start fraction, 2, divided by, 25, end fraction kilograms of tofu in each serving of his famous tofu dish. He has 1\dfrac{1}{10}1
10
1
1, start fraction, 1, divided by, 10, end fraction kilograms of tofu.
Answers
The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings
Unit rateTofu per serving = 2/25 kilogramsTotal tofu Stephen has = 1/10 kilogramsNumber of servings = Total tofu Stephen has ÷ Tofu per serving
= 1/10 ÷ 2/25
= 1/10 × 25/2
= (1×25) / (10 × 2)
= 25/20
= 5/4 servings
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Suppose we want to choose 2 colors, without replacement from 3 colors red blue and green how many ways can this be done in the order of the choice is relevant and not relevant
Answers
The two colors can be chosen in 3 different ways.
In how many ways can we choose two colors?
If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.
Replacing that we get:
[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]
The two colors can be chosen in 3 different ways.
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A square lawn has area 98 ft². A sprinkler placed at the center of the lawn sprays water in a circular pattern as
shown in the figure. What is the radius of the circle?
Answers
The radius of the circle exists approximately 4.95 feet.
How to estimate the radius of the circle?Given the area of the square as A = 98 ft²
The side length of the square choice is equivalent to the diameter of the circle.
First, we must obtain the length of the square.
Area of a square [tex]= L^2[/tex]
98 = L²
L = √98
L = 9.89 ft
Thus the diameter of the circle exists at 9.89 ft
radius = diameter/2
radius = 9.89/2
radius ≈ 4.95 feet
Therefore the radius of the circle exists approximately 4.95 feet.
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For what value of x is the rational expression below undefined x-4/3x2-75
Answers
The given expression is undefined when x = 5 OR x = -5
Undefined expressionFrom the question, we are to determine the value of x for which the given expression is undefined
The given expression is
x-4/3x²-75
An expression is undefined when the denominator equals zero
Thus, the expression is undefined when
3x² - 75 = 0
Now, we will determine the values of x in the equation above
3x² - 75 = 0
3x² = 75
x² = 75/3
x² = 25
x = ±√25
x = ±5
Hence, the given expression is undefined when x = 5 OR x = -5
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For every 6,000 batches of 100 cards that are printed, she examines every 100th batch to make sure the logo is aligned and the magnetic strip works. Identify the population and the sample. a. population: 6,000 batches of 1000 cards sample: every 10,000 cards c. population: 6,000 batches of 1000 cards sample: every 100th batch b. population: 6,000 batches of 100 cards sample: every 10,000 cards. d. population: 6,000 batches of 100 cards sample: every 100th batch
Answers
Using sampling concepts, the population and the sample are given as follows:
d. population: 6,000 batches of 100 cards sample: every 100th batch.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:
The population is: All New York State residents.The sample is the 1000 randomly selected New York state residents.Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.
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find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29
Answers
Answer:
x = 15, UV = 12, SV = 31
Step-by-step explanation:
13 + 6 + (2x - 18) = 4x - 29
2x + 1 = 4x - 29
2x = 30
x = 15
UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12
SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31
f(x) =4x2 + 8x -5 factor completely
Answers
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 11 lb stretches a certain spring 9 in., how much will a force of 22 lb stretch the spring?
Answers
Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The measures are direct proportional, hence the rule of three is:
11 lb - 9 inches
22 lb - n inches
Applying cross multiplication:
11n = 9 x 22
n = 9 x 2
n = 18 inches.
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if the area of the figure below is 400m. find x
Answers
Answer:
it's answer came 20000o
Make sure the answer is 100% correct. Then circle the answer in a circle.
Answers
Answer:
False
Any integers that the numbers 5, 10 , 15 but 20 can be used as a counter argument against the statement.
Step-by-step explanation:
The claim is that A⊆B which stands for that A is a SUBSET in B, or that B contains A.
The truth is that B⊆A since 5 has more possible outcomes than 20 in the number of integers.
So the list of all possible answers are r5, r10, and r15 where N⊆Z.
For example I choose r=3 and r15, 3(15)= 45. I can use the number 45 as a counter argument that the statement of A⊆B is false.
a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answers
Answer:
Step-by-step explanation:
write the expression as the sine or cosine of an angle
pi/5 cos pi/2+sin pi/2\cos pi/5
Answers
The given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
The addition formula for trigonometryThe given expression is:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )[/tex]
Note that:
[tex]sin(A+B)=sinAcosB+cosAsinB[/tex]
Applying the addition principle to the given expression, we have:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
Therefore, the given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
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Consider a situation that you might need to use your understanding of probability to make an informed
decision.
• What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
Answers
The information that can be collected to make an insurance policy will be information regarding the drivers.
How to illustrate the information?It should be noted that the probability simply means the likelihood of the occurence of an event.
In this case, when choosing a car insurance policy, we can use the probability to determine the likelihood for the need to file a claim.
The course of action is to survey a number of drivers to get information from them.
Also, the benefit of this approach is that the food drivers can pay less premium while the disadvantage can be the cost that's involved.
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1. A situation that can use probability to make an informed decision is when deciding on an insurance policy to take.
2. The information that you would collect for an insurance policy decision includes insurance:
PremiumPolicy coveragePolicy limitsDeductiblesDiscounts.3. An understanding of probability helps the policyholder to:
Analyze different insurance policies to determine the best plan to choose amid uncertainty.Measure the likelihood of an event occurring and its consequences.Determine the level of risk involved.4. Possible Benefits and Limitations of Probability:Using probability, the insurance policyholder enjoys these benefits:
Measure outcomesReduce uncertaintyOptimize policiesSpread risk coveragePredict future losses and events.However, the limitations of probability in measuring insurance risks become prominent under the following situations:
Presence of an infinite number of possible outcomes. Where the outcomes are not equally likely.Thus, probability analyzes insurance policies to determine the best plans and their deductible amounts.
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on a number line, suppose point E has a quotient of -1, and EG = 12. what are the possible coordinates of point G?
Answers
-13, or +11, because they are both 12 places away from -1.
A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality 90 greater-than 2.50 (x + 5) to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?
Answers
Answer:
Step-by-step explanation:
x is the number of students
(x+5) is the number of students and chaperons
$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have
2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)
The inequality "90 greater-than 2.50 (x + 5) "
90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign
90 ≥ 2.50(x+5)
A tape manufacturer reduces the price of its Heavy Duty tape from $40 to $38 a reel and the price of Regular tape from $32 to $31 a reel. A computing center normally spends $1600 a month for tapes and 3/5 of this is for Heavy Duty tapes. How much will they save a month under the new prices?
Answers
Answer:
68
Step-by-step explanation:
Lets first find the quantity of tape the computing center is purchasing/month.
3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.
The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.
Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.
24*38=912
20*31=620
912+620=1532
Then to find the money they are saving we subtract the new price from the original price.
1600-1532=68
If 1st and 4th term of G.P is 500 and 32 respectively ,its 2nd term is
Answers
The second term of sequence is 200
Geometric equationGeometric sequence are sequence that differs in their term by a common ratio. The nth term of a geometric sequence is expressed as:
Tn = ar^n-1
where
a is the first term
n is the number of term
If 1st and 4th term of G.P is 500 and 32 respectively, hence;
T1 = ar^0 = 500
T3 = ar^3 = 32
From both expressions, the first term a = 500
Substitute into equation 2
ar^3 = 32
500r^3 = 32
r^3 = 32/500
r = ∛32/500
r = 0.4
Determine the second term
T2 = 500(0.4)
T2 = 200
Hence the second term of sequence is 200
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Sets A and I are defined as follows:
A = {-5, -2,0, 2, 5}
I = {−5, -1, 1, 5, 8}
Find the union of A and I.
Answers
Answer:
{-5,-2,0,2,5,-1,1,8}
Step-by-step explanation:
The union of two sets contains all elements that are in set A or in set B (possibly both).
{-5,-2,0,2,5} ∪ {-5,-1,1,5,8} = {-5,-2,0,2,5,-1,1,8}
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer.
Answers
Answer:
62 inches
Step-by-step explanation:
Since we need to leave 2 cm of room on both sides, the maximum width of TV is 136 - 2 - 2 = 132 cm. Next, use the Pythagorean Theorem, a^2 + b^2 = c^2, to find the diagonal.
132^2 + 86^2 = c^2
c^2 = 17424 + 7396
c^2 = 24820
c = 157.543644746 cm
Finally, convert the value to inches using the given conversion factor.
157.543644746/2.54 = 62.0250569868 inches
Type the correct answer In each box. Round your answers to the nearest tenth.
A ladder is placed 30 Inches from a wall. It touches the wall at a helght of 50 inches from the ground.
The angle made by the ladder with the ground is
(blank) degrees, and the ength of the ladder Is (blank)
Inches.
Answers
Answer:
Angle = 59.03 degrees
Length = 58.3 inches
Step-by-step explanation:
Solutions greatest to smallest for function
=2+5−7
Answers
The greatest or maximum value for the given function = -8.25
The minimum or smallest value for the given function =-4
Calculation of greatest and smallest functionsThe maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,
Formula max = c - (b2 / 4a)
Where,
a = 2
b = 5
C = -7
Therefore maximum function
= -7 -(5*2/4*2)
= -7-(10/8)
= -7 - 1.25
= -8.25
The minimum value of a function is the least value of that function.
Formula for the minimum = c - b^2/4a.
= -7-5^2/4*2
= -32/8
= -4
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5/9+ (-4/5)
A. 1/4
B. 11/45
C. -9/14
D. -11/45
PLEASE HELP ILL GIVE BRAINLIST
Answers
How much would you need to deposit in an account now in order to have $4000 in the account in 15 years? Assume the account earns 4% interest compounded monthly. Round to the nearest cent
Answers
Answer:
$2500
Step-by-step explanation:
CA=p(1+MR÷1200)
4000=p(1+180×4÷1200) 15 yrs =15×12=180 month
4000=1.6p
p=4000÷1.6
p=2500
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What is the standard form equation of an ellipse that has vertices (18,1) and (−10,1) and co-vertices (4,14) and (4,−12)?
Answers
Answer: [tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
Step-by-step explanation:
You first need to determine if the ellipse is horizontal or vertical, which can be found by the length of the major axis.
The vertices are at (18,1) and (-10,1). The distance is 28 units. (horiz)
The co-vertices are at (4,14) and (4,-12) The distance 26 units (vert)
The major axis is horizontal, so the standard form of the ellipse is
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex] where (h,k) are the coordinates of the center.
To find the center, find the midpoint of the major axis [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
The center is at (4,1)
Since the major axis is 2a, a would be 28 divided by 2=14 squared : 196
The minor axis is 2b, so b would e 26/2=13 squared: 169
Inserting the center and a,b values into the standard form eq:
[tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
hope this helps.