Answer:
π/2 + n*π
Step-by-step explanation:
All real numbers except π/2 + n*π
Answer:
Step-by-step explanation:
For some problems, stating the domain actually means to identify what x CANNOT be as opposed to what x IS. This occurs with tangent and cotangent functions along with rational functions.
As far as the tangent function goes, look at your unit circle. Your unit circle gives you 2 values for each angle, the first value reflects the cosine of the angle and the second value reflects the sine of the angle. This is because cosine is directly related to the x values and sine is directly related to the y values; cos goes into the "x" position and sin goes into the "y" position inside the brackets just like x and y go into parenthesis for coordinates. Anyway, a ratio is undefined if the denominator equals 0, right? And since tangent is the same as sin/cos, tangent is undefined when cos is 0. This occurs at [tex]\frac{\pi}{2}+k\pi[/tex] . That means that tangent does NOT exist at pi over 2 and every integer of pi you add in after. Let's look at a couple of examples of how that domain "works". Adding in an integer means adding in 1, 2, 3, etc. If the domain of tangent is undefined at [tex]\frac{\pi}{2}+k\pi[/tex], then let's let k = 1, and
[tex]\frac{\pi}{2}+1\pi=\frac{\pi}{2}+\frac{2\pi}{2}=\frac{3\pi}{2}[/tex] . Now let k = 2:
[tex]\frac{\pi}{2}+2\pi=\frac{\pi}{2}+\frac{4\pi}{2}=\frac{5\pi}{2}[/tex]. Now let k = 3:
[tex]\frac{\pi}{2}+ 3\pi=\frac{\pi}{2}+\frac{6\pi}{2}=\frac{7\pi}{2}[/tex]. And it continues like that.
You can see when you graph the tangent function in radian mode on your calculator that these values where tangent is undefined show up as asymptotes. Use your unit circle and your graphs to determine the domain of trig functions.
At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation \sigmaσ= 180 is assumed known.
Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95% confidence interval estimate of the population mean examination
score if a sample of 200 applications provided a sample mean \overline x
x
= 935?
c. Use the confidence interval to conduct a hypothesis test. Using \alphaα= .05, what is your
conclusion?
d. What is the p-value?
Answer:
(910.053 ; 959.947)
Pvalue = 0.00596
Step-by-step explanation:
Given :
Population mean, μ = 900
Sample size, n = 200
Population standard deviation, σ = 180
The hypothesis :
H0 : μ = 900
H0 : μ ≠ 900
The 95% confidence interval:
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 95% confidence = 1.96
Hence,
Margin of Error = 1.96 * 180/√200
Margin of Error = 24.947
95% confidence interval is :
935 ± 24.947
Lower boundary = 935 - 24.947 = 910.053
Upper boundary = 935 + 24.947 = 959.947
(910.053 ; 959.947)
Hypothesis test :
Test statistic
(935- 900) ÷ (180/√(200))
Test statistic = 2.750
Pvalue from Test statistic ;
Pvalue = 0.00596
Pvalue < α ; Reject H0 and conclude that score has changed
Hence, we can conclude that the score has changed
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
I don’t get this at all
Answer:
0.21
Step-by-step explanation:
There's 21 kids with a cell phone and no tablet
so 21/100 = 0.21
Choose the correct vertex of the function f(x) = x2 - X + 2.
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
please help with the steps thx
Answer:
amount financed: 47800
monthly payment: 454.97
FC: 6796.40
558390.76
198390.76
Step-by-step explanation:
1.)
the amount financed is the cost- amount paid today
61800-14000=47800
effective rate: .027/12=
assuming it's an annuity immediate...
x=payment
[tex]47800=x\frac{1-(1+.00225)^{-(10*12)}}{.00225}\\47800=105.0617517x\\x=454.97[/tex]
going to assume that the last part is asking for the interest
to find the interest do financed amount-total paid
454.97*10*12-47800=6796.4
2.)
Find the effective rate
.056/4=.014
assuming annuity immediate
[tex]6000\frac{(1+.014)^{15*4}-1}{.014}=558390.7595[/tex]
interest earned:
558390.7595-6000*60=198390.76
Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
i need help pls it’s timedd!!!!
Answer:
5.
Step-by-step explanation:
If you were to rotate the triangle, you can apply Pythagoras Theorem.
Therefore,
a^2 = 12^2 - 13^2 (Note: a^2 = a squared)
a^2 = 144 - 169
a^2 = -25.
a = 5.
Not sure why its negative though im pretty sure its the right answer.
in BCD triangle :
DC^2 = BC^2 + BD^2
13^2 = 12^2 + BD^2
169 = 144 + BD^2
BD^2 = 169 - 144
BD^2 = 25
BD = 5
_______________________
In the other hand we have :
BD^2 = AB × BC
5^2 = AB × 12
AB = 25/12
________________________
Also we have :
AD^2 = AB × AC
AD^2 = 25/12 × ( 25/12 + 12 )
AD^2 = 25/12 × ( 25/12 + 144/12 )
AD^2 = 25/12 × 169/12
AD^2 = 25 × 169 / 12 × 12
AD^2 = 5 × 5 × 13 × 13 / 12 × 12
AD = 5 × 13 / 12
AD = 65 / 12
AD = 5.42
Thus the correct answer is option C
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Nếu cắt mặt cầu bởi một mặt phẳng chiếu đứng thì hình chiếu bằng của giao tuyến là:
Answer:
Im sorry I can't understand you
Helppppo plsssssssssss I need helppp with thissss
Answer:
82 is what r equals
Step-by-step explanation:
So, lets go over what we know:
D equals rt, or r * t:
D=r*t
The table shows:
t=2 - d=164
t=3 - d=246
These are the only 2 values we need to look at.
We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:
164= r * 2
Divide both sides by 2 to iscolate r:
82=r
So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:
246=r*3
Divide by 3 to iscolate the r:
82=r
So we know that r must equal 82.
Hope this helps!
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
Select the correct answer.
At a high school there are 53 players on the football team, 15 players on the baseball team, and 12 players on
the basketball team. How many ways can a committee be formed with 1 representative from each team?
Math
Answer:
53*15*12=9540
Step-by-step explanation:
its just 53 times 15 times 12 for all the possibilities.
Say the first football player was picked, same with the first baseball player, and the first basketball player were all picked, then another possiblity would be the first football player, the second baseball player, and the first basketball player, here is a numerical example.
Football Baseball Basketball
1 1 1
1 2 1
1 2 2
1 2 3
1 2 4
and so on including all the patterns it would be 9540 possibilities
The total number of ways of forming a committee by selecting one representative from each team is 9540.
What is combination?
A combination is a mathematical technique that determines the number of possible arrangements or the number of ways in a collection of items where the order of the selection does not matter.
Combination Formula[tex]nC_{r}= \frac{n!}{r!(n-r)!}[/tex]
Where,
[tex]nC_{r}[/tex] is a number of combination.
n is total number of objects in the set.
r is the number of choosing objects from the set.
Multiplication rule in combination?According to the multiplication rule in combination if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions.
According to the given question
Total number of football players = 53
Total number of baseball players = 15
Total number of basket ball players = 12
Therefore,
Number of ways of selecting one representative from football team is given by
[tex]53C_{1} =\frac{53!}{1!52!} = 53[/tex]
Number of ways of selecting one representative from baseball team is given by
[tex]15C_{1} =\frac{15!}{1!14!}=15[/tex]
Number of ways of selecting one representative from basketball team is given by
[tex]12C_{1} =\frac{12!}{1!11!} =12[/tex]
So, the total number of ways of forming a committee by selecting one representative from each team = 53 × 15 × 12 =9540.
Hence, total number of ways of forming a committee by selecting one representative from each team 9540.
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I need help please I dont understand
What is the value of 6 / x + 2x squared when x = 3
Answer:
8
Step-by-step explanation:
The equation will become 6/3+2(3)
-->6/3=2
-->Because of Order of Operation we will multiply the 2 and 3 before adding so 2(3) = 6
--> 6+2=8
Answer:
x=6
Step-by-step explanation:
when its squared you multiply by 2
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
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When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
HELP PLEASE IM STUCK!
1. Which of these describes the relation for this set of coordinate pairs?
{(-1, 5), (12, 18), (0, 6), (-3, 3), (4, ?), (?, 11)}
a. x - y = 6 b. f(x) = x +6 c. f(x) = 6 d. y = 6x e. None of these
Answer:
b) f(x) = x + 6
Step-by-step explanation:
The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)
giải phương trình vi phân: y" - 5y' + 6y = 6x + 7
Неоднородное ДУ второго порядка. Детали в аттаче.
what are functions in math
PLEASE HELP
If the absolute value represents the distance from zero, can we have a negative distance?
Answer:
No, you cannot have a negative distance.
Step-by-step explanation:
No, you cannot have a negative distance.
Let's say you were asked for the absolute value of -4. How many units is -4 away from 0? The answer would be 4. There is no negative distance from 0.
Hope this helps, please mark brainliest! :)
Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
Julie borrowed 3500 for 3years at a seven and a half simple interest rate how much interest rate is that
Answer:
787.50
Step-by-step explanation:
interest=3500*7.5*3/100
interest=35*7.5*3
interest=787.50
Find x. Round to the nearest tenth: 29° 500ft
X=[?]ft
9514 1404 393
Answer:
437.3 ft
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(29°) = x/(500 ft)
x = (500 ft)cos(29°)
x ≈ 437.3 ft
Can I get some help with this question? I have attempted several times and failed.
9514 1404 393
Answer:
B. relative maximum of 8.25 at x=2.5
Step-by-step explanation:
A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...
x = -5/(2(-1)) = 5/2
The value of the extreme is ...
f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25
The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.
The function has a relative maximum of 8.25 at x = 2.5.
__
A graphing calculator can show this easily.
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where What is the probability that at least 5 people attend the meeting given that at least 2 attend
Answer:
The probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,...
What is the probability that at least 5 people attend the meeting given that at least 2 attend?
The explanation of the answer is now provided as follows:
Given:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,... (1)
Since it is given that at least 2 attend, it implies that we need to calculate P(x) at x = 2.
Substituting x = 2 into equation (1), we have:
P(X = 2) = 1 / 2^(2 + 1)
P(X = 2) = 1 / 2^3
P(X = 2) = 1 / 8
P(X = 2) = 0.1250, or 12.50%
Therefore, is the probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
