Answers
Answer:
[tex]\sin L = \frac{3}{5}[/tex]
[tex]\tan N = \frac{4}{3}[/tex]
[tex]\cos L = \frac{4}{5}[/tex]
[tex]\sin N = \frac{4}{5}[/tex]
Step-by-step explanation:
Given
The above triangle
First, we calculate the length LM using Pythagoras theorem.
[tex]LN^2 = LM^2 + MN^2[/tex]
[tex]10^2 = LM^2 + 6^2[/tex]
[tex]100 = LM^2 + 36[/tex]
Collect like terms
[tex]LM^2 = 100 - 36[/tex]
[tex]LM^2 = 64[/tex]
Take positive square root
[tex]LM=8[/tex]
Solving (a): Sin L
[tex]\sin L = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin L = \frac{MN}{LN}[/tex]
[tex]\sin L = \frac{6}{10}[/tex]
Simplify
[tex]\sin L = \frac{3}{5}[/tex]
Solving (b): tan N
[tex]\tan N = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan N = \frac{LM}{MN}[/tex]
[tex]\tan N = \frac{8}{6}[/tex]
Simplify
[tex]\tan N = \frac{4}{3}[/tex]
Solving (c): cos L
This calculated as:
[tex]\cos L = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos L = \frac{LM}{LN}[/tex]
[tex]\cos L = \frac{8}{10}[/tex]
Simplify
[tex]\cos L = \frac{4}{5}[/tex]
Solving (d): sin N
This is calculated using:
If [tex]a + b = 90[/tex]
Then: [tex]\sin a = \cos b[/tex]
So:
[tex]\sin N = \cos L[/tex]
[tex]\sin N = \frac{4}{5}[/tex]
Related Questions
Please help I’ll mark you as brainliest if correct
Answers
Answer:
I think it is 75
Step-by-step explanation:
because you divide 45 by 3 to get 15 then 15 x 5 is 75:)
Step-by-step explanation:
3*15=45
5*15=45
Check the pic please
With steps please
Answers
Answer:
Angle BOD = 75⁰
Step-by-step explanation:
Answer attached...
Hope it helps :)
multiply the binomials (2x+1)(3x+2)
Answers
The Answer is (6x^2+7x+2)
Use the FOIL method
Three triangles are drawn on the same piece of paper such that no two sides are on the same line. What is the maximum number of points of intersection of the three triangles?
Answers
Answer:
6
Step-by-step explanation:
PLEASE HELP ASAP ???
Answers
Answer:
-1
Step-by-step explanation:
If x3=125 and y3=8, what is the value of y−x
Answers
Answer:
X= 5
Y= 2
Y-X= 2-5= -3
Find the distance between the pair of points (3, 5) and (-3, 8)
Answers
Answer: 3
Step-by-step explanation:
What is the area of this trapezoid?
Answers
Answer: 6625 sqaure yards
Step-by-step explanation:
Area for a trapezoid formula is A=(base 1 + base 2)·height÷2
So base one is 120 and base two is 10+120+15=145
and the height is 50 so (120+145)·50÷2=6625 The area for the trapezoid is 6625
Try to answer this question for me pleaseee
Answers
Answer:
H
Step-by-step explanation:
180-48=132
Two students were asked if they liked to read. Is this a good example of a
Yes, this is a good statistical question because a variety of answers
Yes, this is a good statistical question because there are not a varie
No, this is not a good statistical question because there are not a
No, this is not a good statistical question because there are a van
Answers
Answer:
C. No, this is not a good statistical question because there are not a.
Step-by-step explanation:
Because you need a big amount of people to ask for it to be a A good statistical question.Your welcome! Please mark brainliest!
(Or please correct me if I'm wrong)
Write the log equation as an exponential equation. You do not need to solve for x. log(5x+2)=3
Answers
Answer:
So happy you are with brainly
Step-by-step explanation:
34
What is equivalent to -2(x-5)?
Answers
Answer:
-2x+10
Step-by-step explanation:
-2(x-5)
Distribute
-2*x -2*-5
-2x+10
A 30-foot ladder was put up against a building. The ladder makes a 64° angle with the ground. How high up
on the wall does the top of the ladder reach?
Answers
Answer:
height = 26.96 feet
Step-by-step explanation:
sin 64° = height/30
0.8988 = height/30
height = 26.96 feet
The sum of −7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7.
Answers
Answer:
n has no value.
There is no solution to this equation
Step-by-step explanation:
let n be the number
In pieces:
sum of the number and 1: (n + 1)
8 times the sum: 8(n + 1)
-7 times a number: -7n
sum of -7 times and...: -7n + 8(n + 1)
number minus 7: n - 7
the same as: =
All together:
-7n + 8(n + 1) = n - 7
-7n + 8(n+1)=n-7
-7n + 8n+8=n-7
0=-15
Explain what median is and how to solve for it
Answers
Answer: See below
Step-by-step explanation:
Median is the value that separates the higher data and lower data. In simple terms, it is the "middle" value of the whole set of data. There are two different ways to solve for the median.
1. If the data set has an odd number of values, line the values up in increasing order. Then the value or number that lies in the middle will be the median.
For example, if we are given a data set {1, 3, 4, 2, 5}. First, we line them up by increasing order, which becomes {1, 2, 3, 4, 5}. Since it is an odd number set, we can directly get the median which is 3.2. If the data set has an even number of values, line the values up in increasing order. Then there will be two number that lies in the "middle" together. We add them up and divide them by 2. The average of the two numbers will be the median of the set.
For example, if we are given a data set {2, 6, 4, 10, 8, 12}. First, we line them up by increasing order, which becomes {2, 4, 6, 8, 10, 12}. Since it is an even number set, we get our median from the two numbers in the middle, which are {6, 8}. We add them together to get 14 and then divide by 2 which is 7. So the median will be 7.Hope this helps!! :)
Please let me know if you have any questions.
what is the least common denominator of 1/2, 2/3, and 3/8
Answers
Answer: 24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
For the least common denominator, we have to find the smallest number that all fo them multiply to.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
8, 16, 24, 32
i think we can see something
24 is the most common number between them all, so the fractions will be
12/24 (1/2), 16/24 (2/3), and 9/24 (3/8)
Pay the bill using the fewest possible bills/coins
Answers
Answers:
Open the pdf below and youll find what you need. also do the largest bills you can.
The diagram shows the diameter of the opening
of a waffle ice cream cone.
18 cm
Which of the following is closest to the area of
the opening in square centimeters?
A.
1,017.88 cm2
C. 254.47 cm
B.
56.55 cm2
D. 28.27 cm2
I will give brainleist
Answers
Answers
D 36
Step-by-step explanation:
77 is the area for the squared trapezoid and 36 is the closest to 77
Inscribed Angles B
Find each measure.
K
X=
6x
M
L
Answers
Answer:
x = 15
z = 25
Step-by-step explanation:
In [tex] \odot\: O, \: \angle MLK [/tex] is inscribed in a semicircle.
[tex] \therefore m\angle MLK =90\degree [/tex]
[tex] \therefore 6x\degree =90\degree [/tex]
[tex] \therefore 6x =90[/tex]
[tex] \therefore x =\frac{90}{6}[/tex]
[tex] \therefore x =15[/tex]
In [tex] \odot\: A, \: \angle PRQ[/tex] is inscribed in a semicircle.
[tex] \therefore m\angle PRQ =90\degree [/tex]
[tex] \therefore (4z-10)\degree =90\degree [/tex]
[tex] \therefore 4z-10 =90[/tex]
[tex] \therefore 4z =100[/tex]
[tex] \therefore z =\frac{100}{4}[/tex]
[tex] \therefore z =25[/tex]
Kathy bought 5 pencils for the price of $6.30. Which equation represents r, the cost, in dollars, of each pencil?
A.r=6.30+5
B.r = 6.30÷5
C.r=6.30×5
D.r=6.30−5
Answers
9514 1404 393
Answer:
B. r = 6.30÷5
Step-by-step explanation:
The cost per pencil is found by dividing the cost by the number of pencils.
Here, the cost is $6.30 and the number of pencils is 5. Then the cost per pencil (r) is ...
r = 6.30 ÷ 5
Evaluate the indicated limit algebraically. Change the form of the function where necessary. Please write clearly with description of each step, thank you very much.
3x^2+4.5
________
x^2-1.5
lim
x → ∞
Answers
Answer:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Step-by-step explanation:
We want to evaluate the limit:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}[/tex]
To do so, we can divide everything by x². So:
[tex]=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}[/tex]
Now, we can apply direct substitution:
[tex]\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}[/tex]
Any constant value over infinity tends towards 0. Therefore:
[tex]\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3[/tex]
Hence:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:
[tex]\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to\infty}3=3[/tex]
The limit of a constant is simply the constant.
We acquire the same answer.
You purchase a new car for $24,000. If you obtain a 5 year bank loan at 2.75% compounded monthly, what is your monthly loan payment?
Answers
Answer:
The monthly loan payment is of $458.88.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Amount owed after 5 years:
Loan of 24000 means that [tex]P = 24000[/tex]
5 years means that [tex]t = 5[/tex]
Interest rate of 2.75% means that [tex]r = 0.0275[/tex]
Compounded monthly means that [tex]n = 12[/tex]
The amount is A(5). So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(5) = 24000(1 + \frac{0.0275}{12})^{12*5}[/tex]
[tex]A(5) = 27533[/tex]
What is your monthly loan payment?
$27,533 in 5 years = 5*12 = 60 months. So
27533/60 = 458.88
The monthly loan payment is of $458.88.
Select the correct difference. 5d^2 + 4d - 3 less 2d^2 - 3d + 4
Answers
Answer:
[tex]3d^2+ 7d- 7[/tex]
Step-by-step explanation:
Given
[tex]P_1 = 5d^2 + 4d - 3[/tex]
[tex]P_2 = 2d^2 - 3d + 4[/tex]
Required
P1 less P2
This means that we subtract P2 from P1.
So, we have:
[tex]P_1 - P_2 = 5d^2 + 4d - 3 - (2d^2 - 3d + 4)[/tex]
Remove bracket
[tex]P_1 - P_2 = 5d^2 + 4d - 3 - 2d^2 + 3d - 4[/tex]
Collect like terms
[tex]P_1 - P_2 = 5d^2 - 2d^2+ 4d + 3d- 3 - 4[/tex]
[tex]P_1 - P_2 = 3d^2+ 7d- 7[/tex]
The difference is: [tex]3d^2+ 7d- 7[/tex]
11-square root of x where x=64
Answers
Is this linear, exponential growth, exponential decay, or neither?
Answers
Answer:
exponential decay
Step-by-step explanation:
the y coordinates are getting smaller while x gets bigger so for 1x y is .5 then .25 then .125 etc..
What is the quotient of (x^3 + 8) divided by (x + 2)?
Answers
Answer:
(x^3 +8)/(x+2) = x^2 -2x +4
Step-by-step explanation:
In a study of academic procrastination, the authors of a paper reported that for a sample of 451 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.74 hours and the standard deviation of study times was 3.10 hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.
(a) Construct a 95% confidence interval to estimate μ, the mean time spent studying for the final exam for students taking introductory psychology at this university. (Round your answers to three decimal places.) TWO VALUES
(b) The paper also gave the following sample statistics for the percentage of study time that occurred in the 24 hours prior to the exam.
n = 451 x = 43.78 s = 21.96
Construct a 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam. (Round your answers to three decimal places.)
Answers
Answer:
a) The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
b) The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{3.3}{\sqrt{451}} = 0.305[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7.74 - 0.305 = 7.435 hours
The upper end of the interval is the sample mean added to M. So it is 7.74 + 0.305 = 8.045 hours.
The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
Question b:
90% confidence interval means that [tex]Z = 1.645[/tex]
The margin of error is:
[tex]M = 1.645\frac{21.96}{\sqrt{451}} = 1.701[/tex]
43.78 - 1.701 = 41.079%
43.78 + 1.701 = 45.481%
The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Write 3 ratios equivalent to 2/5
Answers
Answer:
4/10, 6/15, 8/20
Step-by-step explanation:
The average weekly salary of two employees is $5250. One makes $500 more than the other. Find their salaries.
Answers
Answer: thier salaries are $5000 and $5500
Step-by-step explanation:
Let the average weekly salary of one employee be =x
And that of the other employee be = x+500
Such that if thier average of their salaries= $5250
So, their total salary= $5250 x 2=10,500
The equation to solve each employee salary becomes
x+x+500=10,500
2x+500=10,500
2x=10,500-500
2x=10,000
x=10,000 /2
x= first employee salary =$5000
second employee = x+500 =$5500
Which is a function?
O {(-3,5), (1,4), (3,7), (1,7),(4,9)}
O {(7,9), (13,-2), (8,4), (7,0), (4,12)}
O {(2,1),(-1,7), (6,-2), (10,3), (-6,0)}
O {(-2,4), (7,4), (-6,8), (-2,8), (1,1)