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
Find 3 consecutive even integers such that 5 times the second is 82 more than the first .
Answers
Ti best of my understanding the answers are: 1st integers is 18, 2nd is 20, and 3rd is 22.
x is 1st integer
x+2 is 2nd integer
x+4 is 3rd integer
All even
5(x+2)=82+x
5x+10=82+x
5x-x=82-10
4x=72
x=18
1st is x=18
2nd is x+2=18+2=20
3rd is x+4=18+4=22
Good luck.
Many professional sports are arguing that they need a new stadium to be competitive, as newer stadiums can bring in more fan revenue which can in turn allow teams to buy more expensive players. Some major league baseball teams have built new stadiums in the past decade. Consider the attendance (in millions) in the last year of the old stadium and the first year of the new stadium. Using a sample of 5 randomly selected teams, researchers would like to determine if there is any evidence that attendance levels differ between using old vs new stadiums. The data for these five teams are shown below:
Team Attendance (in millions)
Old Stadium New Stadium
Cincinnati Reds 1.9 2.4
New York Yankees 4.3 3.7
Philadelphia Phillies 2.3 3.3
Seattle Mariners 2.7 2.9
Washington Nationals 1.9 2.3
Required:
a. Calculate the test statistic appropriate to the correct statistical method.
b. Suppose all assumptions were satisfied for valid inference, and the researcher found a statistically significant lower average attendance in the new stadium compared to the old stadium. (This does not mean that this data support this conclusion - this is just hypothetical.) Does this mean that the new stadium caused attendance to decrease? Why or why not?
Answers
Answer:
Test statistic = 1.1508
Step-by-step explanation:
Given the data provided
We have to make a table and find d and d²
From the calculations I did in the attachment
n = 5
d² = 1.81
d = 1.5
The t test statistic = 1.5/1.3038 = 1.1505
B. No the new stadium may not have caused the attendance t decrease in this case. Other factors could be responsible for the low attendance.
A shoemaker claims his best product has an average lifespan of exactly 14 years. A skeptical customer asks for evidence (data) that might be used to evaluate this claim. The customer was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 6 years was calculated. Select the 95%, confidence interval for the true mean lifespan of this product.
Answers
Answer:
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0154
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0154\frac{6}{\sqrt{45}} = 1.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.8 = 13.2 years
The upper end of the interval is the sample mean added to M. So it is 15 + 1.8 = 16.8 years.
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.
an exponential function is graphed on the gid. which function is best represented by the graph
a) g(x)=6(1/3)^x
b)g(x)=6(3)^x
c) g(x)=6-(1/3)^x
d) g(x)=6-(3)^x
Answers
Solve the equation. x^x=3/4(√6)
Answers
Answer:
Hi! The answer to your question is [tex]x = 3/2[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
please help i need help
Answers
Answer:
78 I think
Step-by-step explanation:
simply look at the second and third wight see the pattern wich is 7.8 I think and subtract that from the first answer
choosing an ice cream cone from waffle, plain,
or sugar and a flavor of ice cream from
chocolate, vanilla, or strawberry
Answers
Answer:
vanilla,cone
Step-by-step explanation:
Convert 65 degress celsius to degress farenheit.
If necessary, round your answer to the nearest tenth of a degree
Here are the formulas :
C=5/9 ( f-32)
F= 9/5 C+32
Answers
Answer: 150 degrees
Step-by-step explanation:
Answer:
149°F
Step-by-step explanation:
The Celsius measure is 65° . We know the relation between Celsius and Farenheight as ,
⇒ C/5 = F-32/89
⇒ 65/5 = F-32/9
⇒ 13 = F-32 / 9
⇒ F - 32 = 13 × 9
⇒ F = 117 + 32
⇒ F = 149 °F
Hence the Faeenheight measure is 149°F .1. What type of sequence is this? *
3.5, 10.5,31.5, 94.5, 283.5, ---
Arthímetic
Geornetric
Neither
Answers
Answer:
Arthimatic is the answer
Convert 1.375 to decimal fraction؟
Answers
Step-by-step explanation:
11/8 if I'm not wrong
...
Answer:
fgiigdyh
Step-by-step explanation:
can you please help me
Answers
Find the slope,
(5,0) and (0.-7)
Answers
Answer:
[tex]\frac{-7}{-5}[/tex]
-7/-5
is the slope.
or -1 -2/-2
you pick.
Step-by-step explanation:
Δy/Δx
-7-0 / 0-5
-7 / -5
-7/-5
is the slope.
change in y over change in x
y2-y1 over x2-x1
simplify if possible.
-1 -2/-2
it's negative.
Answer:
Slope = 1 2/5 or 1.4
Step-by-step explanation:
Using the y2 - y1/x2 - x1 format, you first replace the variables with the points (5 and 0 can be x1, y1, while 0 and -7 can be x2, y2)
-7 - 0/0 - 5
Now subtract: -7 - 0 = -7; 0 - 5 = -5
You would get -7/-5, which simplified: 1.4 or 1 2/5
:p
there you go!
is 0.70 equal to 7/10
Answers
yes the fraction of .70 is 7/10
Answer:
Yes
Step-by-step explanation:
0.70 = 7/10
Can someone please help me I will mark u brilliant
Answers
Answer:
I believe the answer is 1/12
Step-by-step explanation:
the volume of a rectangular prism is length × width × height
Answer:
[tex] \frac{1}{12} \: cubic \: foot[/tex]
Step-by-step explanation:
[tex]V_{box} = lbh \\ = 1 \frac{1}{2} \times \frac{1}{6} \times \frac{1}{3} \\ \\ = \frac{ \cancel3}{2} \times \frac{1}{6} \times \frac{1}{ \cancel3} \\ \\ = \frac{1}{12} \: cubic \: foot[/tex]
Question 20 (5 points)
All of the pairs of corresponding angles and sides in ACATand ADOG are congruent.
Based on this information, which of the following is a true statement?
A) A DOG has half the area of ACAT.
B) ACATis congruent to ADOG.
C) ADOG has been dilated to form ACAT.
D) There isn't enough information to make a statement about ADOG and ACAT.
Answers
9514 1404 393
Answer:
B) ΔCAT is congruent to ΔDOG
Step-by-step explanation:
If angles are congruent, the triangles are similar. When both corresponding angles and corresponding sides are congruent, the triangles are congruent.
ΔCAT is congruent to ΔDOG
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..
Given the length of segment EB is 12 meters. Find the length of arc EA. Round your answer to the nearest tenth.
Answers
Answer:14.9
Step-by-step explanation:
my calc 3 friend told me
Find the area of the trapezoid. A trapezoid has a base of 8 meters, a height of 6 meters, and a top side length of 4 meters.
Answers
Answer:
36 m²Step-by-step explanation:
A = 1/2(b₁ + b₂)hA = 1/2(8 + 4)*6 = 36 m²find the measure of arc URT
Answers
Hello!
This question is about relating vertical angles and their arc lengths.
Vertical angles have equal angle measures, meaning that they will also have the same arc measure.
We know that arc QR and arc UT have equal angle measures because they are formed with vertical angles.
That means since we know the measure of the other two arcs, which will both be 125 since they are formed with vertical angles, we can solve for the two unknown arc lengths.
A circle is 360 degrees, meaning that we can make the following equation,
[tex]360=QR+UT+125+125[/tex]
[tex]QR+UT+250=360[/tex]
[tex]QR+UT=110[/tex]
Since QR = UT
[tex]QR/UT=55[/tex]
Now, we can solve for arc URT using all the arc measures we have.
[tex]URT=125+55+125[/tex]
[tex]URT=305[/tex]
Hope this helps!
4. Quinn scores 275 points in 5 min on her favorite
video
game. Delilah scores 675 points in 15 min.
If they continue to play at this level, who do you
predict will score 5000 points faster? Explain.
Answers
Answer:
Quinn
For Quinn:
275 points - - > 5 min
5000 points - - > x min
--------------------------------------
275*x=5*5000-->x=90.9 minutes
For Delilah:
675 points - - > 15 min
5000 points - - > y min
--------------------------------------
675*x=15*5000-->y=111.1 minutes
90.9<111.1, so Quinn will score 5000 points faster
Peyton is going to invest $440 and leave it in an account for 5 years. Assuming the
interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Peyton to end up with $520?
Answers
Answer:
The required interest rate would be of 3.4% a year.
Step-by-step explanation:
The amount of money earned in compound interest, after t years, is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
Peyton is going to invest $440 and leave it in an account for 5 years.
This means that [tex]P(0) = 440, t = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 440(1+r)^5[/tex]
What interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $520?
This is r for which P(t) = 520. So
[tex]P(t) = 440(1+r)^5[/tex]
[tex](1+r)^5 = \frac{520}{440}[/tex]
[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{\frac{52}{44}}[/tex]
[tex]1 + r = (\frac{52}{44})^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.034[/tex]
Then
[tex]r = 1.034 - 1 = 0.034[/tex]
The required interest rate would be of 3.4% a year.
The Lane School sold 1,152 granola bars to raise money for digital cameras. All the granola bars were either berry bars or raisin bars. They sold 528 berry bars, and the rest were raisin bars. The granola bars came in boxes of 24 bars. How many boxes of raisin bars did they sell?
Answers
Answer:
26 boxes of raisin bars
Step-by-step explanation:
Take the total bars sold 1152 then subtract the berry bars 528 and you'll get 624. Next you'll divide the 624 by 24 because that's how many that's in a full box. Finally you'll get your answer of 26 boxes.
1152-528=624 ➗ 24 = 26
Plzzz help meeeeeeeeee!
Answers
Answer:
B
Step-by-step explanation:
More students got more than 10 than students that didnt
Lukas is trying to lose weight. He starts the year
weighing 254 pounds. If he plans to burn enough
calories to lose 2 pounds per week, which
equation can be used to find w, the number of
weeks that will pass before Lukas weights 228
pounds?
For BRAINLIST!!
Answers
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Pls help me with this
Answers
Please help with math asap:
Rewrite without parentheses and simplify
(y+7)^2
Answers
y * y = y^2
y * 7 = 7y
7 * y = 7y
7 * 7 = 49
So we have:
y^2 + 7y + 7y + 49
Combine like terms:
y^2 + 14y + 49
write the following comparison as a ratio reduced to lowest terms.
128 hours to 6 days
Answers
Answer:
21.3:1
Step-by-step explanation:
So we have to find the unit rate, and we do that by getting that 6 down to a 1, and we do that by dividing 6 by 6 and then we gotta do that on the other side too:
6 ÷ 6 = 1
128 ÷ 6 = 21.3 (simplified)
So 128 to 6 days in simplest terms is 21.3 hours to 1 day
hope this helps:)
Which letter is the correct answer and why
Answers
Answer:
Option CStep-by-step explanation:
Here,
[Taking 'A' = 'a']
[tex]a \: = \: 4\pi {r}^{2} [/tex]
Then for 'r',
[tex] = > 4\pi {r}^{2} = a[/tex]
[tex] = > {r}^{2} = \frac{a}{4\pi} [/tex]
[tex] = > r = \sqrt{\frac{a}{4\pi} }[/tex]
[tex] = > r = \frac{1}{2}\sqrt{ \frac{a}{\pi} } [/tex]
Hence,
Option C is correct .
A 3 ounces b 4 ounces c 12 ounces or D 15 ounces helps plsss
Answers
Answer:
D 15
Step-by-step explanation:
[tex]\frac{5}{20}[/tex]=[tex]\frac{x}{60}[/tex]
Kaylee is decorating a ballroom ceiling with garland. If the rectangular ceiling is 20 meters by 48 meters, how much garland will Kaylee need to reach from one corner of the ceiling to the opposite corner?
Answers
Answer:
960
Step-by-step explanation: