Which trigonometric function would you use to solve the problem? If S=27° and TR=7 find TS (picture provided)
Answers
Answer:
b. sin or csc
Step-by-step explanation:
Remember that sine trigonometric function is the ratio of the opposite side of a right triangle to its hypotenuse; in other words:
[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]
Also, the cosecant is the inverse of sine, so:
[tex]csc(\alpha )=\frac{1}{sin(\alpha) } =\frac{hypotenuse}{opposite-side}[/tex]
Now, for our triangle, our angle is 27°, the longest side of it is TS, and the opposite side of our angle (27°) is TR; therefore, [tex]\alpha =27[/tex], [tex]hypotenuse=TS[/tex], and [tex]opposite-side=TR[/tex].
Replacing values:
- Using the sine trigonometric function
[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]
[tex]sin(27)=\frac{TR}{TS}[/tex]
[tex]sin(27)=\frac{TR}{TS}[/tex]
[tex]sin(27)=\frac{7}{TS}[/tex]
[tex]TS=\frac{7}{sin(27)}[/tex]
[tex]TS=15.42[/tex]
- Using the cosecant trigonometric function
[tex]csc(\alpha )=\frac{hypotenuse}{opposite-side}[/tex]
[tex]csc(27)=\frac{TS}{TR}[/tex]
[tex]csc(27)=\frac{TS}{7}[/tex]
[tex]TS=7csc(27)[/tex]
[tex]TS=15.42[/tex]
We can conclude that we can use either the sine trigonometric function or the cosecant trigonometric function to solve the problem.
Related Questions
Please answer I’ll rate brainlyest
Answers
Answer:
41.8%
Step-by-step explanation:
From the table, the total number of female patients is given as 335. On the other hand, the total number of female patients with type-O blood is given as 140. The probability that a randomly selected female patient will have type-O blood can be calculated as;
the total number of female patients with type-O blood/the total number of female patients
140/335 = 0.4179
As a percentage this becomes;
0.4179 * 100 = 41.8%
Therefore, the percentage of female patients with type-O blood is 41.8%
Find the area of the following circle. (Round answer to the nearest hundredth.) d = 15 in area = square inches circumference = inches
Answers
The area of a circle with a diameter of 15 inches is 176.63 square inches and the circumference is 47.1 inches, using the formulas A = (pi)r² and C = (pi)d with (pi) approximated as 3.14.
The area and circumference of a circle can be calculated using the formulas A = (pi) r² for the area, and C = (pi) d for the circumference, where r is the radius, d is the diameter, and (pi) is approximately 3.14.
Given the diameter d = 15 inches, we first find the radius by dividing the diameter by 2, which gives us r = 7.5 inches. We then use the area formula to calculate:
Area = (pi) r² = 3.14 ×(7.5 inches)²
Area = 3.14 ×56.25 square inches
Area = 176.625 square inches
After rounding to the nearest hundredth, we get:
Area = 176.63 square inches
For the circumference, we use the formula:
Circumference = (pi) d = 3.14 ×15 inches
Circumference = 47.1 inches
A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned?
Answers
Answer:
54.5 amps to the nearest tenth.
Step-by-step explanation:
V = IR where V = volts, I = current and R = resistance.
12 = I * 0.22
I = 12/0.22
I = 54.5 Amps.
When the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.
The question regarding how many amps will be drawn from the 12-volt battery when a car engine with a resistance of 0.22 ohms is started can be solved using Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. The formula is given by I = V / R.
Therefore, the current drawn from the battery can be calculated as follows:
Voltage (V) = 12 voltsResistance (R) = 0.22 ohmsCurrent (I) = V / R = 12 / 0.22 = 54.55 ampsSo, when the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.
John starting playing video games as soon as he got home from school. He played video games for 15 minutes. Then, it took John 45 minutes to finish his homework. When John finished his homework, it was 3:15 P.M. What time did John get home from school?
Answers
Answer:
2:15
Step-by-step explanation: First you - 15 by 3:15 which = 3:00 then - 45 by 3:00 or 60 - 45 = 15. so therefore 2:15 is the answer. Have a good day, hope I helped
Erica went shopping for art supplies. The watercolor set was 30% off its regular price of $20.00. What did she pay for the watercolors?
Answers
Answer:
$14.00
Step-by-step explanation:
30% less than 100% of the regular price is 70% of the regular price.
Erica paid ...
0.70 · $20.00 = $14.00
The location of point V is (-3,3). The location of point X is (9,13). Determine the location of point W which is 3/4 of the way from V to X
Answers
ANSWER
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
EXPLANATION
We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.
The x-coordinate of this point is given by:
[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]
[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]
[tex]x= \frac{21 - 12}{4 + 3} [/tex]
[tex]x= \frac{9}{7} [/tex]
The y-coordinates is given by;
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]
[tex]y= \frac{39+12}{4 + 3}[/tex]
[tex]y= \frac{51}{7}[/tex]
Hence
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
Answers
Answer: b) rolled three times, number of 2s rolled
d) rolled twice, number of odds rolled
Step-by-step explanation:
A binomial experiment must meet the following criteria:
There must be a fixed number of trials (rolls) Each trial (roll) is independent of the others There are only two outcomes (success or fail) The probability of each outcome remains constant from trial to triala) rolled twice --> satisfies #1 & #2 (n = 2)
X is the sum --> fails #3 (more than two outcomes)
b) rolled three times --> satisfies #1 & #2 (n = 3)
X is the number of 2s rolled --> satisfies #3 & #4 (P success = 1/6)
c) rolled an unknown number of times - fails #1
d) rolled twice --> satisfies #1 & #2 (n = 2)
X is the number of odds rolled --> satisfies #3 & #4 (P success = 1/2)
There are 10 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible
Answers
Final answer:
The number of different subcommittees possible from a board of 10 members when forming a subcommittee of 3 members is 120, calculated using the combination formula C(10, 3).
Explanation:
To calculate the number of different subcommittees possible from a board of directors consisting of 10 members when forming a subcommittee of 3 members, we must use the concept of combinations because the order of selection does not matter. This is a problem of counting without regard to the order and is solved by using the combination formula:
C(n, k) = n! / (k! * (n-k)!) where 'n' is the total number of items to choose from, 'k' is the number of items to choose, 'n!' represents the factorial of n, and 'k!' is the factorial of k.
Here, 'n' is 10 (the total number of board members) and 'k' is 3 (the number of members to be chosen for the subcommittee). Thus, the formula for our calculation is:
C(10, 3) = 10! / (3! * (10-3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Therefore, there are 120 different subcommittees possible when selecting 3 members from a board of 10.
Final answer:
To find the number of different subcommittees possible from 10 members when selecting 3, the combination formula C(n, k) = n! / (k! * (n - k)!)is used, which results in 120 different subcommittees.
Explanation:
The student's question pertains to combinatorics, which is a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Specifically, the student is asking about the number of ways to form a subcommittee of 3 members from a larger committee of 10 members. To solve this, one would use the combination formula, which is used for selecting items from a group without regard to the order in which they are selected.
The combination formula is given by:
C(n, k) = n! / (k! * (n - k)!)
Where:
n is the total number of items to choose from (in this case, 10 board members),
k is the number of items to choose (in this case, a subcommittee of 3 members),
n! (n factorial) is the product of all positive integers up to n,
k! (k factorial) is the product of all positive integers up to k,
(n - k)! is the factorial of the difference between n and k.
Applying the formula to the student's scenario:
C(10, 3) = 10! / (3! * (10 - 3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
So, there are 120 different subcommittees possible when choosing 3 members from a board of 10 members.
If the coefficient of determination for a data set is 0.25 and the SEA for the data set is 12, what is the SST for the data set
A. 16
B. 20
C. 8
D. 12
Answers
Answer:
A
Step-by-step explanation:
We can use a simple formula to solve for SST. The formula is:
[tex]SST=\frac{SSE}{1-R^2}[/tex]
Where
the coefficient of determination is [tex]R^2[/tex]
Now, we are given [tex]R^2[/tex] is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:
[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]
correct answer choice is A
After the program was completed, the coach monitored each of the 30 athletes for five athletic events. At the end of this process, he reported that the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program. What can be concluded from the coach's report?
Answers
Answer:
B
Step-by-step explanation:
A study estimates the cost of tuition at the university will increase by %2.8 each year. The cost of tuition at the university in 2015 was $33,741
Answers
The compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.
How do you calculate compound interest?If n is the number of times the interest is compounded each year and r is the yearly rate of compound interest, the final amount after 't' years is:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
The function b(x) is expressed as follows:
[tex]\rm b(x) = 33741(1+\frac{0.028}{1} )^x\\\\[/tex]
Where ;
Rate(r)=2.8 percent
Total after x years(b)
Initial amount ( P)= 33741
x represents the number of years since 2015.
Hence, the compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.
To learn more about compound interest;
https://brainly.com/question/1329401
#SPJ2
Different sized containers are filled with oil. Later, vinegar is added to make a salad dressing. The ratio used is 1 tablespoon of vinegar (y) to 0.5 tablespoons of oil (x). Which of the following statements is true?
The function is y = 2x because the recipe calls for a ratio of 2 parts oil to 1 part vinegar.
The function is y = 2x because the recipe calls for a ratio of 2 parts vinegar to 1 part oil.
The function is y = 1/2x because the recipe calls for a ratio of 2 parts oil to 1 part vinegar.
The function is y = 1/2x because the recipe calls for a ratio of 2 parts vinegar to 1 part oil.
Answers
the answer is the second one
Answer:
The answer is b!!
Hyperbolas
label the foci, the vertices, and the asymptotes.
(y−3)^2/1 - (x+2)^2/4 = 1
Answers
let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}[/tex]
now let's check for the asymptotes.
[tex]\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2[/tex]
Which best explains why this triangle is or is not a right triangle?
Answers
Answer:
It is a right triangle.
Step-by-step explanation:
By the Inverse Pythagoras Theorem if 39^2 = 36^2 + 15^2 then it is a right triangle.
39^2 = 1521
36^2 + 15^2 = 1296 + 225 = 1521.
So it is a right triangle.
Based on the converse of the Pythagorean Theorem, the triangle with the following side lengths is a right triangle.
What is the Converse of the Pythagorean Theorem?
The converse of the Pythagorean Theorem states that a triangle is a right triangle if the sum of the squares of two of its legs are equal to the square of the length of the longest side (hypotenuse).
The longest side in the triangle is 39 in. Therefore:
39² = 36² + 15²
1,521 = 1,521
Based on this, we can conclude that the triangle given is a right triangle.
Learn more about the converse of the Pythagorean Theorem on:
https://brainly.com/question/9676498
#SPJ2
Which expressions are equivalent to the one below? Check all that apply
64^x
A. 8^2*8^x
B. (8*8)^x
C. 8*8^2x
D. 8*8^x
E. 8^2x
F. 8^x*8^x
Answers
Answer:
B, E, F
Step-by-step explanation:
Equivalent expressions are expressions which are equal. To show expressions are equal, reduce to lowest terms by simplifying using exponent rules.
A. 8^2*8^x = 8^2+x
B. (8*8)^x = 64^x
C. 8*8^2x = 8^(2x +1)
D. 8*8^x = 8 ^ (x+1)
E. 8^2x = 64^x
F. 8^x*8^x = 8^(x+x) = 8^(2x) = 64^x
Answer:
8^2x 8^x (8•8)^x
Step-by-step explanation:
Find the first four iterates of the function f(x) = 3x - 7 with an initial value of x0 = 4.
a.
-5, -8, -17, -44
c.
5, 8, 17, 44
b.
-7, -11, -15, -49
d.
7, 11, 15, 49
Answers
Answer:
c. 5, 8, 17, 44
Step-by-step explanation:
Put the given number into the formula and do the arithmetic:
3·4 -7 = 5 . . . . . matches answer choice C only
___
You know the correct answer at this point. You can check the other numbers if you wish:
3·5 -7 = 8
3·8 -7 = 17
3·17 -7 = 44
Chantelle had signed up for hockey. Her parents set a limit of $400 for costs for the season. It costs $250 to sign up plus $5 for each ice-time. What is the maximum number of ice-times that Chantelle can go to.
Answers
Answer:
30 times
Step-by-step explanation:
subtract 250 from 400, then divide the number (150) by 5 to get your answer 30.
After jogging 3 miles bobby checked his heart rate he counted 30 beats and 15 seconds what would his heart rate be for one minute
Answers
Answer:
Step-by-step explanation:
First, i would add 15 until you get to 60, or divide.
15 / 60 = 4
Then multiply 30 by 4: 30 X 4 =120.
120 is the awnser.
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math, which of the following properties will you use?
associative
commutative
distributive
Answers
14.(22) = 14.(20 + 2)
We still have 14 multiplying 22 but now it will multiply it by 20 and sum it after multiply by 2
So we have the distributive proppertie.
Answer:
distributive property.
Step-by-step explanation:
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math
22 is written as 20+2
so we got 14(20+2)
to multiply this we distribute 14 inside the parenthesis
we multiply 14 with 20 and then multiply 14 with 2
we are distributing 14 inside the parenthesis so its distributive property.
N a flower garden, there are 4 tulips for every 8 daisies. If there are 32 tulips, how many daisies are there?
Answers
Answer: 64 daisies
Step-by-step explanation:
8 x 4 = 32 8 x 8 = 64 daisies
A new car is purchased for 19900 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 8 years?
Answers
Answer:
[tex]\$10,665.64[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$19,900\\r=7.5\%=0.075\\x=8\ years[/tex]
substitute the values in the formula
[tex]V=\$19,900(1-0.075)^{8}=\$10,665.64[/tex]
Answer: The answer is 10665.64
Step-by-step explanation:
Exponential Functions:
y=ab^x
A= starting value = 19900
r=rate = 7.5%=0.075
Exponential Decay:
b=1-r=1-0.075=0.925
Write Exponential Function:
y=19900(0.925)^x
Plug in time for x:
y=19900(0.925)^8
y= 10665.6404317
Evaluate
y≈10665.64
What are the ratios for sin A and cos A? The triangle is not drawn to scale.
Answers
Answer:
The answer is B
Step-by-step explanation:
Find h(-3) if h(x) = x^2 - 2x - 5
Answers
Final answer:
To calculate h(-3) for the function h(x) = x² - 2x - 5, we plug in -3 for x and simplify to get a result of 10.
Explanation:
To find h(-3) when given h(x) = x² - 2x - 5, we need to substitute x with -3 into the function and simplify:
h(-3) = (-3)² - 2(-3) - 5
= 9 + 6 - 5
= 15 - 5
= 10.
Therefore, h(-3) equals 10.
How many females with college degrees work at his two stores?
Answers
Answer:
30
Step-by-step explanation:
At the northside store there are 12 females with college degrees
At the southside store there are 18 females with college degrees
The total number of females at the two stores with college degrees is
12+18 = 30
What is the value of tan A.
Answers
Answer:
15/8.
Step-by-step explanation:
Tan A = opposite / adjacent side
= 15/8.
The value of tan A is 15/8.
What is Trigonometry?It is a mathematical functions which deals with the angles and sides of the right angle triangle.Trigonometric functions include, sine, cosine, tangent, cotangent, secant and cosecant.
Given: Right angled triangle
AB = 8
AC = 17
BC = 15
We have to find tan A.
We know,
tan A = Opposite side / Adjacent side
In the given right angle triangle:
Opposite side = BC
Adjacent side = AB
⇒ tan A = BC/AB
⇒ tan A = 15/8
Therefore, the value of tan A is 15/8.
Learn more about Trigonometry here: https://brainly.com/question/13882808
#SPJ2
125 freshman, 85 passed the english test, 95 passed statistics test, 15 failed both what is the probability that they passed both
Answers
Answer:
0.56
Step-by-step explanation:
125 in total.
Let x be the number of those who passed both tests.
85 passed English, then 85-x passed only English;95 passed statistics, then 95-x passed only statistics;15 failed both.Thus,
x+(85-x)+(95-x)+15=125,
195-x=125,
x=70.
Thus, the probability that they passed both tests is
[tex]Pr=\dfrac{70}{125}=\dfrac{14}{25}=0.56.[/tex]
Match the input values on the left (X) with the output values on the right (Y).
y = 2x + 7
1 11
2 13
3 9
4 15
Answers
Answer:
1 9
2 11
3 13
4 15.
Step-by-step explanation:
When x = 1 y = 2(1) + 7 = 9.
x = 2, y = 2(2)+7 = 11
x = 3, y = 2(3) + 7 = 13
x = 4, y = 2(4) + 7 = 15.
Maddie wants to build a circular fence around her yard. The yard has a radius of 7 feet, what is the circumference? Use 3.14 for π.
A) 43.96
B) 53.86
C) 99.02
D) 100.12
Answers
Answer:
43.96 ft, or about 44 ft
Step-by-step explanation:
C = 2πr. Here, π is approx. 3.14 and r is 7 ft. Thus, the circumference of the yard is
C = 2(3.14)(7 ft) = 43.96 ft
Answer:
it is A
Step-by-step explanation:
I REALLY NEED HELP!! WILL MARK BRAINLIEST!
Which question is best modeled with a division expression?
A. How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?
B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?
C. How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?
D. How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?
Answers
Choice D, because you would have to divide 3 1/2 by 2 to find the answer
the rest are either subtraction or multiplication
Answer:
Option D is best modeled with a division expression
Step-by-step explanation:
A) How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?
Cost of 1 pound = $2
Cost of 3 and 1/2 pounds = [tex]2 \times 3.5[/tex]
B) B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?
1 pie requires 3.5 apples
So, 2 pies requires apples = [tex]3.5 \times 2[/tex]
C) How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?
Recipe requires 3.5 apples
You have 2 apples
More apples required = 3.5 - 2
D) . How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?
Apples required in 2 pies = 3.5
Apples required in 1 pie = [tex]\frac{3.5}{2}[/tex]
Hence Option D is best modeled with a division expression
Find the measure of x for this shape.
A. 36
b.28
c.32
d.22
Answers
let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.
The same is true for the isosceles triangle on the right side. Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.
Check the picture below.