Answer:
60
Step-by-step explanation:
Information needed: a whole circle is 360 degrees.
Explanation: you need a protractor to see how many degree's it is
1. Prove the following identity:
—> sin^2 theta (1+ 1/tan^2 theta) =1
9514 1404 393
Explanation:
[tex]\sin^2(\theta)\times\left(1+\dfrac{1}{\tan^2(\theta)}\right)=\\\\\sin^2(\theta)\times\left(1+\dfrac{\cos^2(\theta)}{\sin^2(\theta)}\right)=\\\\\dfrac{\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta))}{\sin^2(\theta)}=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}[/tex]
Line segment TV is a midsegment of ∆QRS. What is the value of n in the triangle pictured?
A: 6.5
B: 7.6
C: 15.2
D: 3.2
Answer:
D. 3.2
Step-by-step explanation:
Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.
Based on this theorem, we have: TV = ½(RS)
TV = 3n - 2
RS = n + 12
Substitute
3n - 2 = ½(n + 12)
Multiply both sides by 2
2(3n - 2) = (n + 12)
6n - 4 = n + 12
Collect like terms
6n - n = 4 + 12
5n = 16
Divide both sides by 5
5n/5 = 16/5
n = 3.2
4)In order to set rates, an insurance company is trying to estimate the number of sick daysthat full time workers at an auto repair shop take per year. A previous study indicated thatthe standard deviation was2.2 days. a) How large a sample must be selected if thecompany wants to be 92% confident that the true mean differs from the sample mean by nomore than 1 day
Answer:
A sample of 18 is required.
Step-by-step explanation:
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 - 0.92}{2} = 0.04[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.04 = 0.96[/tex], so Z = 1.88.
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.
A previous study indicated that the standard deviation was 2.2 days.
This means that [tex]\sigma = 2.2[/tex]
How large a sample must be selected if the company wants to be 92% confident that the true mean differs from the sample mean by no more than 1 day?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.88\frac{2.2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.88*2.2[/tex]
[tex](\sqrt{n})^2 = (1.88*2.2)^2[/tex]
[tex]n = 17.1[/tex]
Rounding up:
A sample of 18 is required.
Whoever gets this problem right with proper work shown will get brainliest
Answer:
100 % or 1
Step-by-step explanation:
There are two dice
Each dice has a possible roll of 1,2,3,4,5,6
The possible sums are 2,3,4,5,6,7,8,9,10,11,12
The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1
Are the two figures similar? if they are, solve for the missing side.
Answer:
They are not similar.
Step-by-step explanation:
26 / 13 = 2
24 / 11 = 2.18
They are not proportional which means that they don't have a scale factor and cannot be answered.
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
Please help me thank you!!!
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
Anyone willing to help on this worksheet?
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
A jewelry box is in the shape of a rectangular prism with an area of 528 cubic inches. The length of the box is 12 inches and the height is 5 1/2 inches. What is the width of the jewelry box? A=LxWxH
please help. :)
Which value of a in the exponential function below would cause the function to stretch?
f(x) = (1)
O 0.3
O 0.9
O 1.0
O 1.5
Answer:
1.5
Step-by-step explanation:
Took the test already.
The value of a for which the exponential function below would cause the function to stretch is a > 1 Or 1.5.
What are some rules for function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
We know an exponential function f(x) = [tex]e^x[/tex].
Now if we multiply f(x) by some number 'a' which is greater than 1 let it be g(x) = [tex]ae^x[/tex] the function would stretch horizontally for a > 1.
learn more about function transformations here :
https://brainly.com/question/13810353
#SPJ6
The line parallel to y = -3x + 4 that passes through (9,-6)
Answer:
y=−3x+21
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
Which of the SMART criteria are NOT met by this data analytics project goal (pay close attention to whether the options are words the SMART acronym stands for)?
Answer:
Specific
Step-by-step explanation:
The data analytics is defined as the study of analyzing the raw data and information so as to make a proper conclusion about the information. It is a process of inspecting, transforming, and modelling the data with the intention of finding useful information and conclusions.
The acronym for S.M.A..R.T is Specific, Measurable, Attainable, Relevant and Time bounding.
The SMAR criteria which do not meet the data analytics project goal in the question is "Specific".
What is the following product?
(V12+ V6 (16-V10
6-12-2130+6-2V15
-2 དུ་
6V3-615
31/7- V22+2/3-4
2V3+6-2V15
Answer:
The answer is A: 6√2 - 2√30 + 6 - 2√15
Believe me it right.
A certain cosine function has an amplitude of 7. Which function rule could model this situation?
Answer:
y = 7cos bx
Step-by-step explanation:
For a cosine function without pahse shift and vertical shift, but with amplitude given, it will also have period and thus , the formula for the cosine function is;
y = Acos bx
Where;
A is the amplitude
Period = 2π/b
Now, we are told that the amplitude is 7. Thus;
y = 7cos bx
D
6
5
F
5.5
к.
6.6
What additional information must be known to prove the triangles similar by SSS?
A) No additional information is needed.
B) 2D = LJ
C) The lengths of DG and JL
D) .F.LK
Answer:
C) the length of DG and JL
it takes engineer 3 hrs to drive to his brother's house at an average of 50 miles per hour. if he takes same route home, but his average speed of 60 miles per hour, what is the time, in hours, that it takes him to drive home?
Answer:
t2 = 2.5 hours.
Step-by-step explanation:
The distance is the same.
d = r * t
The rates and times are different so
t1 = 3 hours
t2 = X
r1 = 50 mph
r2 = 60 mph
r1 * t1 = r2*t2
50 * 3 = 60 * t2
150 = 60 * t2
150 / 60 = t2
t2 = 2.5
Answer:
Answer: Travel Time is 2 hours & 30 minutes
Step-by-step explanation:
Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles
Original Distance is 150 miles, New Speed is 60 mph.
Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph
please help me with this question.
What two things have to be true in order to use the Zero Product Property?
A: Both sides of the equations must be zero.
B: One side of the equation must be a factored polynomial, and the other side must be -1.
C: One side of the equation must be a factored polynomial, and the other side must be 1.
D: One side of the equation must be a factored polynomial, and the other side must be zero.
Wrong answers will be reported. Thanks!
Answer:
D - One side is a factored polynomial and the other side is 0.
A - Incorrect; If each side is 0, the equation would be equal since 0 = 0.
B - Incorrect; It cannot be -1 because the property states Zero product which means 0 should be the product.
C - Incorrect; It cannot be 1 because the property states Zero product which means 0 should be the product.
D - Correct; One side is 0, and the other is a factored polynomial, which correctly displays the correct definition of Zero Product Property.
A particular fruit's weights are normally distributed, with a mean of 344 grams and a standard deviation of 10 grams. If you pick 10 fruit at random, what is the probability that their mean weight will be between 334 grams and 354 grams
Answer:
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 344 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 344, \sigma = 10[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{10}{\sqrt{10}}[/tex]
What is the probability that their mean weight will be between 334 grams and 354 grams?
This is the p-value of Z when X = 354 subtracted by the p-value of Z when X = 334.
X = 354
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{354 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
X = 334
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{334 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = -3.16[/tex]
[tex]Z = -3.16[/tex] has a p-value of 0.0008.
0.9992 - 0.0008 = 0.9984
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
The function ƒ(x) = x−−√3 is translated 3 units in the negative y-direction and 8 units in the negative x- direction. Select the correct equation for the resulting function.
Answer:
[tex]f(x)=\sqrt[3]{x}[/tex] [tex]3~units\: down[/tex]
[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]
[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]
----------------------------
Hope it helps..
Have a great day!!
Answer:
its not B that what i put and i missed it
Step-by-step explanation:
Giving BrainleYst. Which Inequality is graphed on the coordinate plane?
O A. y<-2x-1
OB. y>-2x-1
OC. ys-2x-1
OD. y2-2x - 1
Answer:
A. y<-2x-1
Step-by-step explanation:
not C or D because it is a dashed line meaning the linear equation will either have the symbol ≥ or ≤.
when y is less than, you shade below
thus, the answer is A
You start savings a $250 a month for the next 22 years to give us a gift to your daughter when she graduates college if you put the money into a long-term savings account that receives 3.5 interest how much money will you be able to give your daughter
Answer:
$376,475.71
Step-by-step explanation:
FVA Due = P * [(1 + r)n – 1] * (1 + r) / r
FVA Due = 250 * [(1.2916)264 – 1] * (1.2916) / .2916
write your answer in simplest radical form
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
A punch contains cranberry juice and ginger ale in the ratio 5:3. If you require 32 L
of punch for a party, how many litres of cranberry juice and how many litres of ginger
ale are required?
Let (-5, 2) be a point on the terminal side of 0.
Find the exact values of coso , csco, and tano.
Answer:
Following are the response to this questions:
Step-by-step explanation:
Please find the graph file in the attachment.
Given:
P=2
B=-5
H=?
[tex]H=\sqrt{P^2+B^2}[/tex]
[tex]=\sqrt{2^2+(-5)^2}\\\\=\sqrt{4+25}\\\\=\sqrt{29}\\\\[/tex]
Using formula:
[tex]\to \ cosec \theta \ or\ \ csco \theta =\frac{H}{P}\\\\\to \cos \theta=\frac{B}{H}\\\\\to \tan \theta=\frac{p}{B}\\\\[/tex]
So,
[tex]\to \ cosec \theta \ or\ \ csco \theta =\frac{\sqrt{29}}{2}\\\\\to \cos \theta=\frac{-5}{\sqrt{29}} =\frac{-5}{\sqrt{29}}\times \frac{\sqrt{29}}{\sqrt{29}}=-\frac{5\sqrt{29}}{29}\\\\\to \tan \theta=\frac{2}{-5}= -\frac{2}{5}\\\\[/tex]
describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point
Answer:
Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation: