Answers
======================================================
Work Shown:
We can apply the law of cosines
a^2 = b^2+c^2-2*b*c*cos(A)
(sqrt(5))^2 = (sqrt(2))^2+(3)^2-2*(sqrt(2))*(3)*cos(A)
5 = 2+9-6*(sqrt(2))*cos(A)
5 = 11-6*(sqrt(2))*cos(A)
11-6*(sqrt(2))*cos(A) = 5
-6*(sqrt(2))*cos(A) = 5-11
-6*(sqrt(2))*cos(A) = -6
(sqrt(2))*cos(A) = -6/(-6)
(sqrt(2))*cos(A) = 1
cos(A) = 1/(sqrt(2))
cos(A) = sqrt(2)/2
A = 45 degrees
Use the unit circle for the last step.
Interestingly, this triangle has only one angle that is a whole number. The other two angles are approximate decimal values.
Related Questions
Is this a function graph
Answers
Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that a given software user will call technical support is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Answers
Answer:
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
100% probability that greater than 26 out of 124 software users will call technical support.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Out of 124 software users
This means that [tex]n = 124[/tex]
Assume the probability that a given software user will call technical support is 97%.
This means that [tex]p = 0.97[/tex]
Conditions:
[tex]np = 124*0.97 = 120.28 \geq 10[/tex]
[tex]n(1-p) = 124*0.03 = 3.72 < 10[/tex]
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
Consider the probability that greater than 26 out of 124 software users will call technical support.
The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0[/tex]
1 - 0 = 1
100% probability that greater than 26 out of 124 software users will call technical support.
Which word describes the relationship of the points (3, 1)
and (3, 6)?
OA) collinear
OB) parallel
C) perpendicular
OD) coincident
Answers
9514 1404 393
Answer:
A) collinear
Step-by-step explanation:
"Parallel" and "perpendicular" are descriptors of pairs of lines and planes. They do not apply to pairs of points.
The two points have different coordinates, so are distinct, rather than coincident.
Of these words, the only applicable choice is "collinear."
__
Additional comment
Any pair of distinct points is collinear. Two points define a line, and two points on the same line are collinear.
Prove that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0 Hint: Apply the First Derivative Test and Fermat's Theorem to the function g=f'
Answers
is a point of inflection, the concavity
changes at x=c
Therefore, f′′(x) changes signs at x=c.
Thus, by the First Derivative Test, f′ has a local extremum at x=c
Hence, by Fermat's Theorem f′′(c)=0
We can conclude that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0.
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
We can prove this statement using the First Derivative Test and Fermat's Theorem.
First, we know from the First Derivative Test that at a point of inflection, the first derivative of the function (in this case, f') must equal 0. Therefore, at the point (c, f(c)), f'(c) = 0.
Next, we can apply Fermat's Theorem. This theorem states that if a function f has a local maximum or minimum at c, then f'(c) = 0. Since the point (c, f(c)) is a point of inflection, we can apply Fermat's Theorem to say that f'(c) = 0.
Now, since f'' exists in an open interval that contains c, we can use the fact that if f'(c) = 0, then f''(c) = 0.
Therefore, we can conclude that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0.
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solve for P assume that none of the denominators are equal to 0
Kl=y(f/p+n + r/u)
Answers
Step-by-step explanation:
KI=yf/p+n + yr/u
(p+n) KI - yrp/u -yrn/u = yf
pKI - yrp/u = yf - nKI + yrn/u
p(KI - yr/u) = yf - nKI + yrn/u
p = (1/KI-yr/u)(yf-nKI+yrn/u)
What is force? How is it measured? Write any two effects of force
Answers
Answer: Please refer to:
- A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. ... Forces only exist as a result of an interaction.
- Force is a vector quantity, with both direction and magnitude. It is defined as Mass x Acceleration = Force.
+ The SI unit of force is the newton (N); defined as the unit of force which would give to a mass of one kilogram an acceleration of 1 meter per second squared.
- two effects of force:
+ It can change the state of movement of the body on which force is applied, i.e. it can move a stationary object or stop a moving object.
+ It can change the shape and size of an object.
Step-by-step explanation:
I'm not sure but hope it helps.
A survey on Internet usage was conducted among a group of 200 students in the school cafeteria. It was found that 100 students spend at least two hours online every day. Which of these is an example of descriptive statistics? a.) 50% of the students in the cafeteria spend at least two hours online each day. b.) 50% of the students in the school spend at least two hours online each day. c.) 50% of the students in a class spend at least two hours online each day. d.) 50% of the students surveyed spend at least two hours online each day.
Answers
Answer:
D) 50% of the students surveyed spend at least two hours online each day.
50% of the students surveyed spend at least two hours online each day.
Hence option d is correct.
Given that,
Number of students who spend at least two hours online = 100
Total number of students surveyed = 200
To calculate the percentage of students who spend at least two hours online each day,
we can use the formula:
percentage = (number of students who spend at least two hours online / total number of students surveyed) x 100%
Plugging in the values from the problem, we get:
percentage = (100 / 200) x 100% = 50%
Therefore, we can conclude that 50% of the students surveyed spend at least two hours online each day.
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What triangle is this
Answers
HOPE SO IT HELPS YOU
Answer:
Isosceles.
Step-by-step explanation:
It's an isosceles triangle because 2 sides are congruent ( 2 are 23 yds long).
Using your textbook, solve the problems below. Show your work.
Solve for y:
y + 8 = 2
Answers
Answer:
i dont know lol
Step-by-step explanation:
2. Which of the following statements contains a quotient?
O A. 7-6 = 1
B. 42 : 6 = 7
C.7 x 6 = 42
O D. 7 + 6 = 13
Mark for review (Will be highlighted on the review page)
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MacBook Air
Answers
a quotient is the number resulted from dividing
please mark brainliest
what percent is 50cent of 50cent
Answers
what
Step-by-step explanation:
pretty sure its 25 percent
Answer:
25%
Step-by-step explanation:
if you take half of 50 it is 25 so all of it is used or 25%
Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3
Point A lies outside of plane P. How many planes can be drawn that pass through point A?
A. 0
B. an infinite number
C. 2
D. 1
Answers
Answer:
D.
Step-by-step explanation:
.
The number of planes that can be drawn that pass through point A is 1.
How to estimate the number of planes that can be drawn that pass through point A?
A perpendicular line creates an angle of 90° with a line or a plane. If a line exists to be drawn from a point to a line or a plane it can only be one. In this case, a line exists to be drawn through a point A to a plane P. If the line stands to be perpendicular, then it exists only one.
Therefore, the correct answer is option D. 1.
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A survey is sent out to 500 people asking questions related to the link between religion and sexual behavior at a young age. The survey does not have any tracking device, and the results are sent to a database that gives no indication of who or where the results came from. However, the database is posted online for religion and human behavior researchers to freely conduct statistical analyses. The responses to this survey are
a. both confidential and anonymous.
b. confidential only.
c. anonymous only.
d. neither confidential nor anonymous.
Answers
Answer:
c
Step-by-step explanation:
Since the the identities of the survey takers were kept secret, it would be anonymous. If it wasn't anonymous, then people would know who took the survey.
Since the survey results were released online for analyses, it is not confidential. If it were to be confidential, then the survey distributors would have kept the results to themseles.
letter A represents the decimal
Answers
Answer:
answer is 0.4
Step-by-step explanation:
HELP ME OUT ASAPPP PLSSS
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Answer:
https://linksharing.samsungcloud.com/ul5cX9oOmhzt
ko dung may tinh hay so sanh
3√7 vs 7√3
Answers
Answer:
what this makes bi sense haha
Step-by-step explanation:
but ok
The distribution of SAT scores is approximately normal with a mean of 1500.
If 1628 is the 90th percentile, what is the standard deviation?
Answers
Answer:
Hello,
Answer
[tex]\sigma=457,95...[/tex]
Step-by-step explanation:
p(z<a)=0.9
p(z<1.29)=0.9015
p(z<1.28)=0.8997
using linear interpolation: with 4 decimals
p(z<1.282)<0.9
[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]
In a group of 50 students, 12 play basketball and volleyball
, 9 play volleyball
and soccer, 8 play basketball and play soccer, and 4 play all 3 sports.
Altogether, 21 play basketball, 22 play volleyball, and 19 play soccer. How
many of the 50 students don't play any of the 3 sports?
Answers
Answer:
17 don't play any
Step-by-step explanation:
12+9+8+4=33
33-50=17
Factorize:
3a^2 + 10a + 3
Answers
Answer: (3a + 1) (a + 3)
Step-by-step explanation:
Concept:
Here, we need to know the idea of factorization.
It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.
Solve:
Given = 3a² + 10a + 3
STEP ONE: separate 3a² into two terms
3a
a
STEP TWO: separate 3 into two terms
3
1
STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.
3a 1
a 3
When cross multiply, 3a × 3 + 1 × a = 10a
STEP FOUR: combine the expression horizontally to get the final factorized expression.
3a ⇒ 1
a ⇒ 3
(3a + 1) (a + 3)
Hope this helps!! :)
Please let me know if you have any questions
Suppose A and B are events with P(A) = 1/4, P(B) = 1/3 and P(A cup B)= 1 2 a ) Find P(A cap B) b) Find P(A|B)
Answers
Answer:
Step-by-step explanation:
Four students each ran 100 m in a 400-m relay race. The team’s total was 49.44 seconds. Find the average time of each runner.
Answers
the average time of each runner is 12.36
Answer:
12.36 seconds
Step-by-step explanation:
Total time = 49.44 seconds
Students = 4
Average = 49.44/4 = 12.36 seconds
Answered by GAUTHMATH
I need help thanks you!
Answers
I think its C: 2 hours. sry if its wrong
Yemi earns 8000naira a month and Bisi earns 6000naira a month. Find the ratio between their income.
Answers
Answer:
8:6
or
4:3
Step-by-step explanation:
help please! willing to give brainly and 5 stars
Answers
Answer:
The answer is 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2/5x-8/5y+x+½y
2/5(1)-8/5(-6)+1+½(-6)
2/5+48/5+1-3
10-2
8
How many different 6-digit phone numbers do not contain the digit 8? Assume that any digit in the phone number can be any of the remaining numbers.
Answers
16)dry air is trapped in a narrow uniform glass tube by a mercury pellet of length 25cm .when the tube is placed vertical with the open end um long.what is the external pressure if the column of air becomes 40 cm in length when inverted ? . ( required answer = 74cm hg )
Answers
Step-by-step explanation:
Ru Tu yulyryosuyyyhlsgjpcbmb kvjvlcykxnlvdlbvhck
chgkbhlxyovk m.
chchhlzixhvkh
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind
Answers
Answer:
540 miles/hr and 50 miles/hr respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
Work out how many more skirts were sold on Friday than on Thursday ?
Answers
Answer:
15 more were sold on friday then thursday
Step-by-step explanation:
what is 9/10 + 7/15
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{9}{10}+\dfrac{7}{15}}[/tex]
[tex]\large\textsf{FIRST: FIND the LCD (Lowest Common Denominator) then solve}\\\large\textsf{from there!}[/tex]
[tex]\large\textsf{If you have calculated it correctly, you should have came up with \underline{\bf 30}}\\\large\textsf{as your LCD (Lowest Common Denominator).}[/tex]
[tex]\mathsf{= \dfrac{9\times3}{10\times3}+ \dfrac{7\times2}{15\times2}}[/tex]
[tex]\mathsf{9\times3=\bf 27}\\\mathsf{10\times3=\bf 30}\\\\\mathsf{7\times2=\bf 14}\\\mathsf{15\times2=\bf 30}[/tex]
[tex]\mathsf{= \dfrac{27}{30}+\dfrac{14}{30}}[/tex]
[tex]\mathsf{= \dfrac{27+14}{30}}[/tex]
[tex]\mathsf{27+ 14=\bf 41}\\\\\mathsf{30+0=\bf 30}[/tex]
[tex]\mathsf{= \dfrac{41}{30}}\large\textsf{ which you could convert to }\mathsf{1 \dfrac{11}{30}}[/tex]
[tex]\boxed{\boxed{\large\textsf{ANSWER: }\bf \dfrac{41}{30} \large\textsf{ or }\mathsf{\bf 1 \dfrac{11}{30}\large\textsf{ because they both equal the same thing}}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, the area would be increased by 98 ft^2. How
much must be added to each dimension?
Let x be the amount that is added to each dimension. After writing an equation in standard form with a > 0, a= ? b= ? and c= ?
(Simplify your answers.)
Answers
Answer:
Step-by-step explanation:
new length=15+x
width=19+x
then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²
original area=15×19=285 ft²
then 285+98=x²+34x+285
or
x²+34x-98=0
x²+34x+17²=98+17²
(x+17)²=98+289=387
x+17=√387=3√43
x=3√43-17 ft
