Find sin 0, where is the angle shown.
Give an exact value, not a decimal approximation.
Answers
Answer:
[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]
Step-by-step explanation:
Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:
[tex]\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:
[tex]a^2+b^2=c^2[/tex]
Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.
Substitute:
[tex](5)^2+b^2=(13)^2[/tex]
Solve for b:
[tex]b=\sqrt{169-25}=\sqrt{144}=12[/tex]
So, the opposite side measures 12.
Then sine will be:
[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]
Related Questions
how can the position of a certain value in a given set of data be described and used in solving real-life problems?
Answers
Percentiles
Assume that the elements in a data set are rank ordered from the smallest to the largest. The values that divide a rank-ordered set of elements into 100 equal parts are called percentiles.
An element having a percentile rank of Pi would have a greater value than i percent of all the elements in the set. Thus, the observation at the 50th percentile would be denoted P50, and it would be greater than 50 percent of the observations in the set. An observation at the 50th percentile would correspond to the median value in the set.
Quartiles
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. The chart below shows a set of four numbers divided into quartiles.
Eight numbers: 1, 2, 3, 4, 5, 6, 7, 8
Note the relationship between quartiles and percentiles. Q1 corresponds to P25, Q2 corresponds to P50, and Q3 corresponds to P75. Q2 is the median value in the set.
While measures of central tendency, dispersion, and skewness are used often in statistics, there are other methods of characterizing or describing data distributions or portions that are commonly used as well. We will examine several of these statistical measures, some of which you may already know or have seen elsewhere.
Standard Scores (z-Scores)
A standard score (aka, a z-score) indicates how many standard deviations an element is from the mean. A standard score can be calculated from the following formula.
z = (X - μ) / σ
where z is the z-score, X is the value of the element, μ is the mean of the population, and σ is the standard deviation.
Here is how to interpret z-scores.
A z-score less than 0 represents an element less than the mean.
A z-score greater than 0 represents an element greater than the mean.
A z-score equal to 0 represents an element equal to the mean.
A z-score equal to 1 represents an element that is 1 standard deviation greater than the mean; a z-score equal to 2, 2 standard deviations greater than the mean; etc.
A z-score equal to -1 represents an element that is 1 standard deviation less than the mean; a z-score equal to -2, 2 standard deviations less than the mean; etc.
John finances his daughter's college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16th through the 19th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero. Calculate X.
Answers
Answer:
Monthly payment = 241.925
Step-by-step explanation:
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
Solving, we have i = 0.6434% monthly approximately
To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18. We therefore conclude that the "future values" fall on the same day, and that they are equal.
We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts. By the end of the operations, one will balance the other (they are equal).
We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.
F(A,i,n) = A*((1+i)^n-1)/i
Step 1:
calculate the future value of the withdrawals
A = W = 25000 (annual withdrawal)
i = 8% (effective annual interest)
n = 4 years (beginning of 16,17,18,and 19th years)
F(A,i,n) = A*((1+i)^n-1)/i
= 25000( (1+0.08)^4 - 1)/(0.08)
= 112652.80
This is also the total deposit after eighteen years.
Step 2:
calculate the future value of the annual deposits D
A = D (total of annual deposits)
i = 8% (effective annual interest)
n = 18 years
Future value of deposits
F(A,i,n) = A*((1+i)^n-1)/i
= D( (1+0.08)^18 -1 ) / 0.08
= 37.45024373981167D
Since this must equal the total withdrawal, we equate the two to calculate D.
37.45024373981167D=112652.80
and solve for D
D = 112652.80 / 37.45024373981167
= $3008.0659
Step 3
Calculate monthly deposit, X
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
The actual monthly interest rate is therefore
i = 1.08^(1/12)-1
Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by
D = X*((1+i)^n-1)/i
3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)
or the monthly amount
X = $3008.0659 / ( 1.08^(1/12)-1)
= 241.925 per month.
=
Pls help I’ll give u some of those brain things
Answers
Answer:
THE ANSWER IS NOT C / 3
THE ANSWER IS "A"
Step-by-step explanation:
all the "hard" work is done (the numbers)...
lets start with the "units" at the end of the problem you have to have mm/day... so just start crossing out "top to bottom" when you see the same unit on the top and bottom... if you se day in the numerator and day in the denominator cross them out...
Do that and the one that has mm on the top and day on the bottom is the answer...
Step #2 ... two of the answers have that ... so now look for "silly fractions"
something like 1 year/ 999 days... your problem does not have totally silly things like that , but the WRONG answer has 1mm/ 10 cm (or something like that ) there is 10 mm in 1 cm, you choices has that opposit in one answer.
how do i solve this using multi-step ?
Answers
Answer:
x=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(x−4)=2(−2x+1)
(3 )(x)+(3 )(−4)=(2) (−2x)+(2) (1)(Distribute evenly)
3x+(−12)=−4x+2
3x−12=−4x+2
Step 2: Add 4x to both sides.
3x−12+4x=−4x+2+4x
7x−12=2
Step 3: Add 12 to both sides.
7x−12+12=2+12
7x=14
Step 4: Divide both sides by 7.
7x /7 =14 /7
x=2
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
Answers
Answer:
0.625 liters
Step-by-step explanation:
Given data
volume drained= 2.5Liters
Time= 4 days
Now the if 4 days leakage will produce a volume of 2.5Liters
Then 1 day will produce a volume of x liters
cross multiply
4x= 2.5
x= 2.5/4
x= 0.625 liters per day
Hence, each day will produce 0.625 liters
David is six times older than Janet. If David is 48 years old, how old is Janet?
Answers
Answer:
David is six times older than Janet. If David is 48 years old, how old is Janet? Janet is 8 years old.
Step-by-step explanation:
48÷6=8
PLEASEEEEEEEEEEE HELPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
1.04
$45,552
Step-by-step explanation:
new price = 1.04 * original price
new price = 1.04 * 43,800
newprice: $45,552
ajdjsjnsjsjdjxhdjdjdjdjdjsjsjsjssjs
Answers
Step-by-step explanation:
The area of a square is given by :
A = a²
Where
a is the side of the square
For square A, Area = 64 sq units
64 = a²
a = 8 units
For square B, Area = 30 sq units
30 = a²
a = [tex]\sqrt{30}[/tex] units
For square C, Side length = 14 units
A = 14²
A = 196 sq units
For square D, Side length = [tex]\sqrt{30}[/tex] units
A = [tex](\sqrt{30})^2[/tex]²
A = 30 sq units
Hence, this is the required solution.
if m 7=99 degrees and m 1=32 degrees then what is m 4 + m 5
Answers
Answer:
229°
Step-by-step explanation:
(180- 32) + (180 - 99)
148 +81
= 229°
first answer gets most brainley
Answers
Answer:
What are we supposed to do on this
Step-by-step explanation:
Answer: the dilated point will be 2 units at the right of P, and 3 units above P.
Step-by-step explanation:
What additional information is needed to prove the triangles congruent by SSS
Answers
Answer:
Angle a = Angle D
Answer:
A: Angle A Angle D
Step-by-step explanation:
Make the scale balanced.
Answers
(5-2)9=27
The answer is 27
They both need to equal the same number to be equal
The ratio of coloured papers to wight papers is 3:8.If there are 48 wight papers, how many coloured papers are there?
Answers
Answer: The total number of colored papers is 18.
Step-by-step explanation:
Given: The ratio of coloured papers to wight papers is 3:8.
Let total number of colored papers = 3x
and total number of wight papers = 8x
Since, there are 48 wight papers , then
[tex]8x=48[/tex]
[tex]\Rightarrow\ x=6[/tex]
Now , number of colored papers = 3(6)=18
Hence, the total number of colored papers is 18.
pls pls pls help don't ignore imma fail
Answers
Answer:
6 as b
7 as a
Step-by-step explanation:
if indeed the scale is 3 to 1, this is correct! the answer is B
Please help me on this problem, im struggling
Answers
Answer:
a
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
in fact if we look at the graph we can see that sausages are 7.5 % and mushrooms 5%, while in the table this datas are inverted.
Please help me with this question...
Answers
Answer:
my answer is in this picture. sorry about my presentation and English
у X -7 -5 -5 -4 -3 -2 ברן 4 LO- To 2 -3 -6 -7 In this graph, the v-intercept of the line is 1. The equation of the line is v=
Answers
Answer:
The y intercepts is -2
y = 1x-2
Step-by-step explanation:
The y intercept is where it crosses the y axis
The y intercepts is -2
We need to determine the slope, by using to points on the line
(0,-2) and (2,0)
m = (y2-y1)/(x2-x1)
= (0 --2)/(2-0)
= (0+2)/(2-0)
= 2/2
= 1
The equation for the line is
y = mx+b where m is the slope and b is the y intercept
y = 1x-2
Evaluate the expression 4 to the power of 3 ÷ (7 − 3) × 2.
Answers
Answer:
5.0625 is 1.5 to the fourth power
Answer:
8
Step-by-step explanation:
4 to the power of 3 is 64.
64 ÷ (7 − 3) × 2
64 ÷ (4) × 2
64 ÷ 8
8
Your answer is 8.
I hope this helps, have a nice day.
Solve. -3 + 9x = 24 pls help 15 pts!!! ASAP
Answers
Answer:
hope it is helpful to you
What does b stand for in this equation?
3b=12
A 1
B 2
C 3
D 4
Answers
Answer:
4
Step-by-step explanation:
3b=12
Divide each side by 3
3b/3 =12/3
b =4
Answer:
D. 4Step-by-step explanation:
Given,
3b = 12
=> b = 12 ÷ 3
=> b = 4 (Ans)
Jenna sells apples and pears. If 20 apples and 60 pears re sold every hour, there will be 80 pears when all the apples are sold. If 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold. How many pears are there at the stall?
Answers
Answer:
There are 1,360 pears.
Step-by-step explanation:
Suppose that there are P pears and A apples.
We know that:
"If 20 apples and 60 pears are sold every hour, there will be 80 pears when all the apples are sold."
Suppose that all of these are sold after N hours, then:
20*N = A
80*N = P - 80
We also know that:
"if 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold."
60*N = A
20*N = P - 400
Then we have four equations:
20*N = A
80*N = P - 80
60*N = A
20*N = P - 400
From the first one and the second one, we get:
20*N = A = 20*N = P - 400
A = P - 400
Now we have 3 equations:
80*N = P - 80
60*N = A
A = P - 400
Now we can just replace the third equation into the second one, then we get:
60*N = A = P - 400
Now we have two equations:
80*N = P - 80
60*N = P - 400
Now, remember that we want to find the number of pears, so we want to find the value of P.
To do it, we can take the quotient of the two equations, so we get:
(80*N)/(60*N) = (P - 80)/(P - 400)
8/6 = (P - 80)/(P - 400)
Now we can solve this for P
(8/6)*(P - 400) = P - 80
(8/6)*P - (8/6)*400 = P - 80
(8/6)*P - P = (8/6)*400 - 80
(2/6)*P = (8/6)*400 - 80
P = (6/2)*( (8/6)*400 - 80 )
P = 3*( (8/6)*400 - 80 ) = 1,360
There are 1,360 pears.
PLEASE PLEASE PLEASE SOMEONE HELP ME THIS IS DUE TODAY
EXPLAINING YOUR ANSWER = BRAINLIEST
What is m∠E?
Answers
Answer:
try 144
Step-by-step explanation:
m<E is basically just ot asking you to find the angle of E, i think :').
And since all angles equal to 180, 180-36=144
(hope ots right)
which are like terms
will give brainest if correct
Answers
Answer:
3ad³
Step-by-step explanation:
Like terms have same variables with same powers.
12ad³ and 3ad³ has same variables a and d³
I hope this helps
4,570= 3thousands+___hundreds+ 7 tens
Answers
Answer: 4 thousands, 5 hundreds, 7 tens
Step-by-step explanation: 4,570 is pretty easy to break down. The first place value is 0 so nothing for that. As you have it there the tens place values has 7. Next is hundreds and there's a 5 there so 5 hundreds. If the number is 4,570 then it should be 4 thousands not three.
Please answer properly.
Answers
Answer:
1) [tex]b=6[/tex]
2) [tex]m=4[/tex]
3) [tex]p=12[/tex]
4) [tex]x=-1\frac{2}{6}[/tex]
Step-by-step explanation:
[tex]b+6=12[/tex]
subtract 6 from both sides
[tex]b=6[/tex]
---------->>>>
[tex]9m=32+4[/tex]
combine like terms
[tex]9m=36[/tex]
divide both sides by 9
[tex]m=4[/tex]
---------->>>>
[tex]21=p+9[/tex]
Subtract 9 from both sides
[tex]12 = p[/tex]
---------->>>>
[tex](10+5)+3x=0[/tex]
Add within the parenthesis
[tex]5+3x=0[/tex]
subtract 5 from both sides
[tex]3x=-5[/tex]
divide both sides by 3
[tex]x=-1\frac{2}{6}[/tex]
Hope this is helpful to you.
No links<3
Fill in the missing value!
Answers
Answer:
2.6 and 3
Step-by-step explanation:
The values of the years are being multiplied by 1.3. So when you multiply 2 by 1.3 you would get 2.6. The years are going up by 1 so the year after 2 would be 3.
Today,high tide measured 5.5 ft and low tide measured 1 ft. What is the amplitude of a cosine function modeling the depth of the water in feet as a function of time in hours
Answers
Answer:
[tex]A = 2.25ft[/tex]
Step-by-step explanation:
Given
[tex]High = 5.5ft[/tex]
[tex]Low = 1ft[/tex]
Required
The amplitude (A)
This is calculated as:
[tex]A = \frac{1}{2}(High - Low)[/tex]
So, we have:
[tex]A = \frac{1}{2}(5.5ft - 1ft)[/tex]
[tex]A = \frac{1}{2} * 4.5ft[/tex]
[tex]A = 2.25ft[/tex]
write the set of positive perfect square numbers that is less than 120 . any sort of help is appreciated due 5 pm
Answers
Answer:
{1,4,9,16,25,36,49,64,81,100}
fjhghdjd ffjfnfnfjdj
Answers
Answer:
$77.90
Step-by-step explanation:
The range between the highest and lowest is 27.50 so the lowest should be 27.50 less than 105.40. 105.40-27.50=77.90
So the lowest pay is $77.90
Write an equation that passes through the points (3, 6) and (1,-1)
Answers
m = y2 - y1
x2 - x1
= -1 - 6
1 - 3
= -7 / (-2)
= 7/2
y = m(x - x1) + y1
y = 7(x - 3) + 6
2
2y = 7x - 21 + 12
2y = 7x - 9
Answer:
y = 7/2x - 9/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - 6 / 1 - 3
-7 / -2
7/2
y = 7/2x + b
-1 = 7/2(1) + b
-1 = 7/2 + b
-9/2 = b
