Answers
Answer:
n = √3
m = √3
Step-by-step explanation:
The triangle is an isosceles right triangle with 2 equal base angles of 45° each.
Thus:
Reference angle = 45°
Hypotenuse = √6
Opposite = m
Adjacent = n
✔️To find m, apply the trigonometric function SOH, we have:
Sin 45 = opp/hyp
Sin 45 = m/√6
√6 × 1/√2 = m (sin 45 = 1/√2)
√6/√2 = m
√(6/2) = m
√3 = m
m = √3
✔️To find n, apply the trigonometric function, CAH:
Cos 45 = adj/hyp
Cos 45 = n/√6
√6 × √2/2 = n (cos 45 = √2/2)
√12/2 = n
√(4*3)/2 = n
(2√3)/2 = n
√3 = n
n = √3
Related Questions
The Washington Monument in Washington, D.C. is surrounded by a circle of 50 American flags that are each 100 feet from the base of the monument. The distance from the base of a flag pole to the top of the monument is 564 feet. What is the angle of elevation from the base of a flag pole to the top of the monument?
Answers
Answer:
Step-by-step explanation:
cosx=100/564
x=arccos(100/564)
x=79.79 degrees (to the nearest hundredth of a degree)
The angle of elevation from the base of a flag pole to the top of the monument is to be considered as the 79.79 degrees.
Calculation of the angle of elevation;Since there is 100 feet from the base of the monument.
And, The distance from the base of a flag pole to the top of the monument is 564 feet
Now the angle should be like
cosx = 100/564
x = arc cos(100/564)
x=79.79 degrees
hence, The angle of elevation from the base of a flag pole to the top of the monument is to be considered as the 79.79 degrees.
Learn more about an angle here: https://brainly.com/question/124950
You put $500 in a savings account. The account earns $20 simple interest in 6 months. What is the annual interest rate? Write your answer as a percent
Answers
Answer:
8%
Step-by-step explanation:
For simple interest, we use the equation I = PRT, where I is the interest earned, P is the principal/amount invested, R is the rate as a decimal, not percentage, and T is the time in years.
For this problem, we have to use 0.5 for T, because 6 months is 1/2 a year.
20 = (500)(r)(0.5)
20 = 250r
r = 0.08 = 8%
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
help din HDKE EJFNQKEHWHQODBEHQVEIFNFJRNSJEBSG
Step-by-step explanation:
di ko din alam e AHAHAHAHAHAHAHAHAHA NSKFBWJF S DJEBEJS
JSHEBEJS IF JENSKS.DJWKW
SBWUKWVEUEBJQBRJDNDJXBDJDBDKW
EBEJE KD DJWKQKQBWHS
Can someone tell me what x and y would be
Answers
Step-by-step explanation:
20°+120°+I°=180°
I=40°
using sine rule,
I/sin I=x/sinX
12/sin40=x/sin20
x=12sin20/sin40
x=6.4
using similarly and enlargement,
we have, cw/cp=y/120
8/12=y/120
y=80°
Please help I’m on a test
“Given the triangle below, what is the longest side length?”
Answers
~11.31
Pythagorean Theorem because it is a right triangle.
This is due in 10 minutes please help me
Answers
Given:
The rate of interest on three accounts are 7%, 8%, 9%.
She has twice as much money invested at 8% as she does in 7%.
She has three times as much at 9% as she has at 7%.
Total interest for the year is $150.
To find:
Amount invested on each rate.
Solution:
Suppose x be the amount invested at 7%. Then,
The amount invested at 8% = 2x
The amount invested at 9% = 3x
Total interest for the year is $150.
[tex]x\times \dfrac{7}{100}+2x\times \dfrac{8}{100}+3x\times \dfrac{9}{100}=150[/tex]
Multiplying both sides by 100, we get
[tex]7x+16x+27x=15000[/tex]
[tex]50x=15000[/tex]
Dividing both sides by 50, we get
[tex]x=\dfrac{15000}{50}[/tex]
[tex]x=300[/tex]
So, the amount invested at 7% is [tex]300[/tex].
The amount invested at 8% is
[tex]2(300)=600[/tex]
The amount invested at 9% is
[tex]3(300)=900[/tex]
Hence, the stockbroker invested $300 at 7%, $600 at 8%, and $900 at 9%.
which of the following is NOT a property of all parallelograms
(1) the diagonals are perpendicular
(2) the diagonals bisect each other
(3) opposite sides are congruent
(4) adjacent angles are supplementary
Answers
10
Sara was thinking of a number. Sara adds 19 to it, then doubles it and gets an answer of 39.2. What was the original number?
Answers
Answer:
0.6
Step-by-step explanation:
2(x+19)=39.2
x+19=19.6
x=0.6
what is the density of the oak board? it is 5.5 inches wide, 1.5 inches thick and 3 feet long
Answers
multiply 5.5 the width with 1.5 by 3 which gives you 24.75 inches feet long.
5.5 x 1.5 x 3=24.75 that's your answer.
Answer:297 cubic inches, other person is incorrect.
Step-by-step explanation:5.5 inches* 1.5inches * 3 feet
Convert 3 feet to inches and you have 36 inches. So now it becomes 5.5inches*1.5inches*36inches = 297 cubic inches
The diameter of a circle is 18 cm. Find the circumference to the nearest tenth to the nearest tenth.
Answers
c=2πr. r=18/2=9
=2 ×22/7 ×9
=56.6 to the nearest tenth
Find the distance between (−9, 7) and (−6, 7).
Answers
Answer:
(6,7),(9,6)
Step-by-step explanation:
HOPE THIS HELPS!!!!
A number is divided by 3 and decreased by 5 is 6. What is the number???
Answers
Answer:
Given : x/3-5=6
answer = 23
Step-by-step explanation:
x-5=6*3
x-5=18
x=18+5
x=23
Answer:
33
Step-by-step explanation:
let the number be n , then the number divided by 3 is [tex]\frac{n}{3}[/tex] and decreased by 5
[tex]\frac{n}{3}[/tex] - 5 = 6 ( add 5 to both sides )
[tex]\frac{n}{3}[/tex] = 11 ( multiply both sides by 3 )
n = 33
The number is 33
Which equation is an identity?
Answers
Chicago, Illinois has an elevation of 600 feet. Seely, California is -200 feet. What does 0 represent in the context of this situation?
Answers
Answer:
Sea level
Step-by-step explanation:
In geography, 'Elevation' is measured in relation to sea level, so sea level would be zero.
Thus, Chicago is 600 feet above sea level and Seely, California is 200 feet below sea level.
If there were nothing but flat land all the way from Seely to the ocean, sea water would come in and cover Seely. Fortunately for the people in Seely. California's coastal mountain range is between the town and the ocean, so that does not happen.
Answer:
It represents the "SEA LEVEL"
subtract 15/12and 5/6
Answers
Answer:
5 / 12
Step-by-step explanation:
You must have common denominators in order to add or, in this case, subtract.
Answer:
[tex] \frac{15}{12} - \frac{5}{6} [/tex]
We have a simple formula that can be reduced We will put it into a combined form [tex]1 \times \frac{3}{12} - \frac{5}{6} [/tex]Find a common numerator [tex]1 \times \frac{3}{12} - \frac{10}{12} [/tex]So our answer is [tex] \frac{5}{12} [/tex]PLEASE HELP!!! I WILL GIVE BRAINLIEST
Answers
Answer:x=2y=3
Step-by-step explanation: I did this before
I already know the answer but I want to see if people get it right :) will give brainiest to correct answer.
There is a patch of lily pads on a lake. Every day, the patch doubles in size.
If it takes 48 days for the lily pads to cover the entire lake how much days does it take for the lily pads to cover half the lake.
Answers
Answer:
is it 47? I'm not sure
if not can you explain it to me
Answer:
47 days
Step-by-step explanation:
Since the patch of lily pads double each day, the day before day 48 would cover half of the lake.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previously research has shown the variability in the number to be σ = 2. The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error the researchers need at least:
A. 53 observations.
B. 107 observations.
C. 106 observations.
D. 54 observations.
2.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 100 horses seen beginning on the day the study is funded. The resulting interval is likely biased because:
A. the first 100 horses seen is not an SRS of all horses with enteroliths and therefore never representative.
B. a sample of 100 horses is too small to obtain an unbiased estimate.
C. the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths.
D. All of the above
3.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 20 horses seen beginning on the day the study is funded. The researchers will calculate a 95% confidence interval. The procedure is not valid because the:
A. sample size is too small for the central limit theorem to apply.
B. average number is not an integer and does not reflect any actual observation.
C. None of the above. The procedure is valid.
D. data are counts and, therefore, not Normally distributed.
4.
In a test of hypothesis for a mean, which statement is CORRECT?
A. The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
B. As long as the population distribution consists only of positive values, sample size does not matter.
C. The population distribution can be any distribution because the sample mean is always Normally distributed.
D. The population must be normal because that is the only case when the sample mean is Normally distributed.
5.
A "false negative," in which no effect is detected when in reality one exists, is an example of:
A. a Type I error.
B. the power of the test.
C. a Type II error.
D. None of the above
Answers
Answer:
1.) 107 observations
2.) the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths
3.) A. sample size is too small for the central limit theorem to apply.
4.) The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
5.) a Type I error
Step-by-step explanation:
n = [(Zcritical * σ) ÷ E]²
n = sample size
Zcritical at 99% = 2.58
E = error margin = 0.5
Standard deviation, σ = 2
n = [(2.58 * 2) ÷ 0.5]²
n = [5.16 ÷ 0.5]²
n = (10.32)²
n = 106.5024
n = 107 observations
B.) The thought or decision that the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths will introduce a bias in the study.
C.) For central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
D.) Distribution must be normal it approximately normal, obeying the central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
For f (x) = 2x+1 and g(x) = x2 - 7, find (fºg)(2).
Answers
Answer:
Step-by-step explanation:
Your first step will be to set up the problem:
f(x) - g(x)
Next you will substitute in your values:
(2x + 1) - (x2 - 7)
The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:
2x + 1 - x2 + 7
Then combine your like terms:
2x - x2 + 8
Lastly put your expression in standard form (highest exponent to lowest)
-x2 + 2x + 8
Hope this helped!
Which of the following is the product of (3x − 5) and (3x + 5)?
Answers
Answer:
[tex] {9x}^{2} - 30x + 25[/tex]
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
(3x + 5)(3x - 5)
By using identity
(a + b)(a - b) = a² - b²
3x² - 5²
9x² - 25
I NEED HELP NOW PLZ!!!
Answers
Answer:
A) P' (0, -9)
Step-by-step explanation:
find the greatest common divisor of the numbers 96 and 212
Answers
Answer:
The GCF of 96 and 212 is 4.
please help i don't know this one
Answers
Answer:
Hey do you know the answer to the question you wrote a while ago?
Step-by-step explanation:
(02.05)
Two similar triangles are shown on the coordinate grid:
A coordinate plane is shown. Triangle XYZ has vertices X at negative 5 comma negative 1, Y at negative 6 comma negative 2, and Z at negative 3 comma negative 2. Triangle X double-prime Y double-prime Z double-prime has vertices X double-prime at 10 comma negative 2, Y double-prime at 12 comma negative 4, and Z double-prime at 6 comma negative 4.
Which set of transformations has been performed on triangle XYZ to form triangle X′′Y′′Z′′?
Do you?? :(
Find m∠ABC in the picture. (it's not solving for x.)
Answers
Answer:
20°
Step-by-step explanation:
180-140=40
1/2 of 40=20
Pls help, thank you :)
Answers
3,500,000 divided by 100
That equals
=35000
So (3)
Hope this helped ^^
Answer:
(3)
Step-by-step explanation:
I need help plz hurry before the time is over plz plz
Answers
Answer:
JK
Step-by-step explanation:
As it is shown in the diagram JK is the segment bisector of MN. That means JK cuts MN in half.
Answer pls is mathematically is due today in 1 m
Answers
Answer:
200.96 units^2 or 64π units^2
Step-by-step explanation:
8^2(3.14) = 200.96 units^2 or 64π units^2
(multiplied by 2 to change the radius to diameter)
if x degree + x + 10 degree + x + 15 degree + x + 20 degree + x + 25 degree + x + 30 degree
Answers
Answer:
x° + x° + 10° + x° + 15° + x° + 20° + x° + 25° + x° + 30°
= 6x° + (10 + 15 + 20 + 25 + 30)°
= 6x° + 100
0 = 6x + 100
6x = 100
X = 100/6
X = 16.66
write in set notation; The et of all real numbers greater than 8 but less than 65
Answers
Answer:
{x I 8 < x < 65}
Step-by-step explanation:
{x I 8 < x < 65}
what is -4m+5=5-4m show all solutions
Answers
Answer:
m=0
Step-by-step explanation:
How to solve your question 4 +5=5−4
Step 1: Rearrange Terms 4+5=5−4 4+5=−4+5
Step 2 : Subtract 5 from both sides 4+5=−4+5
-5 -5
Step 3 : Simplify 4m= -4m
Step 4: Add 4m to both sides of the equation 4m= -4m
+4 +4
Step 5: Simplify 8m=0
m=0