Answer:
-1
Step-by-step explanation:
Note that [tex]i+i^2+i^3+i^4 = i-1-i+1 = 0[/tex], and this means that every 4 terms, the terms cancel to 0. Therefore, by taking modulo 4, we only need to find [tex]i^{257}+i^{258}+i^{259} = i-1-i = -1[/tex] since $i$ has a cycle of 4.
9514 1404 393
Answer:
-1
Step-by-step explanation:
Alternate terms have a sum of zero:
i^n +i^(n+2) = (i^n)(1 +i^2) = (i^n)(1 -1) = 0
So, the sum to i^256 is zero, and i^257 +i^259 = 0. The value of the sum is then i^258 = i^(258 mod 4) = i^2 = -1
The given expression evaluates to -1.
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20
Answer:
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
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.
The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.
This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]
Sample of 30:
This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]
What is the probability that the sample mean will be between $7.75 and $8.20?
This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.
X = 8.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = 2.63[/tex]
[tex]Z = 2.63[/tex] has a p-value of 0.9957
X = 7.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = -2.3[/tex]
[tex]Z = -2.3[/tex] has a p-value of 0.0107.
0.9957 - 0.0157 = 0.985
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answer:
"0.250" is the appropriate answer.
Step-by-step explanation:
Given:
New car sample,
= 1453
Preferred foreign,
= 363
Now,
The amount of new automobile purchasers preferring foreign cars will be approximated as:
= [tex]\frac{363}{1453}[/tex]
= [tex]0.250[/tex]
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
PLEASE HELP
Answer:
8
Step-by-step explanation:
As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8
I dont get what this is asking me to do
Answer:
Step-by-step explanation:
what this statement is saying is that if you have
4 x + 3x^2 + 5 + 8x^2 + 12x + 9
that
3x^2 + 8x^2 = 11x^2
4 x + 12x = 16x
5 + 9 = 14
get added together the final answer would be
in descending order as : 11x^2 + 16x + 14
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1
9514 1404 393
Answer:
(b) -1
Step-by-step explanation:
The graph shows the difference between the two expressions is zero at x=-1.
__
Additional comment
For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.
Answer:
The answer is b: -1
Step-by-step explanation:
good luck!
An equation is shown below:
3(4x − 2) = 1
Which of the following correctly shows the steps to solve this equation?
Step 1: 12x − 2 = 1; Step 2: 12x = 3
Step 1: 12x − 6 = 1; Step 2: 12x = 7
Step 1: 7x + 1 = 1; Step 2: 7x = 0
Step 1: 7x − 5 = 1; Step 2: 7x = 6
Step-by-step explanation:
Step 1: 12x-6= 1
step 2:12x=7
Which of the following is the differnce of two squares
What is the measure of F?
G
65
10
H H
10
A. Cannot be determined
B. 55
C. 75
D65
Answer:
D. 65°
Step-by-step explanation:
It is so because the triangle is isosceles, two identical sides and two equal angles.
A homeowner estimates that it will take 11 days to roof his house. A professional roofer estimates that he could roof the house in 6 days. How long will it take if the homeowner helps the roofer?
Answer:
If the homeowner helps the roofer it will take 4 days to roof the house.
Step-by-step explanation:
Given that a homeowner estimates that it will take 11 days to roof his house, while a professional roofer estimates that he could roof the house in 6 days, to determine how long it will take if the homeowner helps the roofer the following calculation must be done:
1/6 + 1/11 = X
0.1666666 + 0.09090909 = X
0.25 = X
1/4 = X
Therefore, if the homeowner helps the roofer it will take 4 days to roof the house.
Find the interval in which y= x2 + 4 is increasing
Answer:
x > 0 and x > -6
[tex]{ \tt{y = {x}^{2} + 4}} \\ { \tt{for \: x > 0 :positive \: integers }} \\ y = 0 < x < {}^{ + } \infin[/tex]
If two marbles are selected in succession with replacement, find the probability that both marble is blue.
Answer:
1 / 9
Step-by-step explanation:
Choosing with replacement means that the first draw from the lot is replaced before another is picked '.
Number of Blue marbles = 2
Number of red marbles = 4
Total number of marbles = (2 + 4) = 6
Probability = required outcome / Total possible outcomes
1st draw :
Probability of picking blue = 2 / 6 = 1 /3
2nd draw :
Probability of picking blue = 2 / 6 = 1/3
P(1st draw) * P(2nd draw)
1/3 * 1/3 = 1/9
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
the point (-2,5) is reflected across the y-axis. which of these is the ordered pair of the image
Answer:(2,5)
Step-by-step explanation: watch this video
https://youtu.be/l78P2Xi68-k
On a shelf at a gaming store, there are three Sony PlayStations and seven Nintendo Wii coasters left. If one gaming system is selected at random, find the probability that the system is a Wii console.
Answer:
hello
as probability is equal to number of favourable outcomes/total number of out comes,
Step-by-step explanation:
=7/10
HOPES THAT IT HELPS YOU
PLEASE MARK ME AS BRAINLIEST
While out for a run, two joggers with an average age of 55 are joined by a group of three more joggers with an average age of m. if the average age of the group of five joggers is 45, which of the following must be true about the average age of the group of 3 joggers?
a) m=31
b) m>43
c) m<31
d) 31 < m < 43
Answer:
they have it on calculator soup
Step-by-step explanation:
Answer:
D. 31<m<43
Step-by-step explanation:
45 x 5 = 225 which is the age of the 5 joggers altogether.
55 x 2 = 110 which is the age of the 2 joggers together.
3m + 110 = 225 then solve for m so,
3m = 115
m = 38.3333
so hence, m is greater than 31 but less than 43.
answer: D
Below are the heights (in inches) of students in a third-grade class. Find the median height. 39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Given:
The heights (in inches) of students in a third-grade class are:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
To find:
The median height.
Solution:
The given data set is:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Arrange the data set in ascending order.
37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53
Here, the number of observations is 16. So, the median of the given data set is:
[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]
[tex]Median=\dfrac{47+48}{2}[/tex]
[tex]Median=\dfrac{95}{2}[/tex]
[tex]Median=47.5[/tex]
Therefore, the median height of the students is 47.5 inches.
(4-1) + (6 + 5) = help plz
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
9514 1404 393
Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
A sprinter travels a distance of 200 m in a time of 20.03 seconds.
What is the sprinter's average speed rounded to 4 sf?
Given:
Distance traveled by sprinter = 200 m
Time taken by sprinter = 20.03 seconds
To find:
The sprinter's average speed rounded to 4 sf.
Solution:
We know that,
[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.
[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]
[tex]\text{Average speed}=9.985022466[/tex]
[tex]\text{Average speed}\approx 9.985[/tex]
Therefore, the average speed of the sprinter is 9.985 m/sec.
Answer:
9.985
Step-by-step explanation:
When Cameron moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 24 inches tall and Tree B was 39 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Answer:
time interval when Tree A is taller than Tree B is;
t > 5 years
Step-by-step explanation:
Tree A;
Initial height = 24 inches
Increase in height per year = 6 inches per year
Thus, for t years after being planted, height is;
A = 6t + 24
Tree B;
Initial height = 39 inches
Increase in height per year = 3 inches per year
Thus, for t years after being planted, height is;
B = 3t + 39
For tree A to be taller than tree B, then it means thay;
A > B
Thus;
6t + 24 > 3t + 39
Subtract 3t from both sides to get;
6t - 3t + 24 > 39
3t + 24 > 39
3t > 39 - 24
3t > 15
Divide both sides by 3 to get;
t > 5
Thus, time interval when Tree A is taller than Tree B is; t > 5
Help me complete the proof!
Answer:
Distributive Property means you can multiply the outside and inside of parenthesis.
Addition Property... means you can add the same value to both sides of the equation without changing it. In this case you add 3x.
Subtraction Property... same as addition property, but with subtraction. In this case subtract 10 from both sides.
Division property... same as addition and subtraction properties but with division. In this case divide both sides by 8.
Technically the addition property can be used for the subtract 10 because you just add -10 and multiplication property could be used for the division, because you just multiply both sides by 1/8, but for the purpose of this equation, you would say subtraction and division.
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!if 3 sec²θ-5tan θ-4=0 find the general solution to this equation
3 sec²(θ) - 5 tan(θ) - 4 = 0
Recall the Pythagorean identity,
cos²(θ) + sin²(θ) = 1.
Multiplying both sides by 1/cos²(θ) gives another form of the identity,
1 + tan²(θ) = sec²(θ).
Then the equation becomes quadratic in tan(θ):
3 (1 + tan²(θ)) - 5 tan(θ) - 4 = 0
3 tan²(θ) - 5 tan(θ) - 1 = 0
I'll solve by completing the square.
tan²(θ) - 5/3 tan(θ)) - 1/3 = 0
tan²(θ) - 5/3 tan(θ) = 1/3
tan²(θ) - 5/3 tan(θ) + 25/36 = 1/3 + 25/36
(tan(θ) - 5/6)² = 37/36
tan(θ) - 5/6 = ±√37/6
tan(θ) = (5 ± √37)/6
Take the inverse tangent of both sides:
θ = arctan((5 + √37)/6) + nπ or θ = arctan((5 - √37)/6) + nπ
where n is any integer
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 2140% of what number is 16.6?
Solve the equation by completing the square.
0 = 4x2 − 72x
Answer:
B
Step-by-step explanation:
Given
4x² - 72x = 0 ← factor out 4 from each term
4(x² - 18x) = 0
To complete the square
add/subtract (half the coefficient of the x- term)² to x² - 18x
4(x² + 2(- 9)x + 81 - 81) = 0
4(x - 9)² - 4(81) = 0
4(x - 9)² - 324 = 0 ( add 324 to both sides )
4(x - 9)² = 324 ( divide both sides by 4 )
(x - 9)² = 81 ( take the square root of both sides )
x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )
x = 9 ± 9
Then
x = 9 - 9 = 0
x = 9 + 9 = 18
Answer:0,18
Step-by-step explanation:
its right
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
