Answers
Answer:
Half angle Identity for cosine:
[tex]$\cos \left(\frac{\theta}{2} \right)=\pm \sqrt{\frac{1+\cos(\theta)}{2} } $[/tex]
[tex]\text{Note that it is} \pm \text{because we don't know which Quadrant the half-angle is, }[/tex][tex]\text{the information of}\cos(\theta) \text{is not enough to conclude the angle}[/tex]
[tex]$\frac{\pi}{8} \text{ is a Quadrant I angle, therefore, positive}$[/tex]
[tex]$\cos \left(\frac{\pi}{8} \right)=\sqrt{\frac{1+\cos(\frac{\pi}{4} )}{2} } $[/tex]
The equation is true.
Related Questions
14. 2057 Q.No. 1(a) Sum to infinity:
1 + 3x + 5x2 + 7x3 +... (-1<x<1).
Answers
The sum appears to be
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n[/tex]
I'll assume you want to find out what function this sum converges to.
Let
[tex]f(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
with -1 < x < 1. Differentiating gives
[tex]f'(x)=\dfrac1{(1-x)^2}=\displaystyle\sum_{n=0}^\infty nx^{n-1}=\sum_{n=1}^\infty nx^{n-1}=\sum_{n=0}^\infty(n+1)x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=f'(x)+xf'(x)[/tex]
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=\frac{1+x}{(1-x)^2}[/tex]
Which of the following is a polynomial?
O A. x2 + 2
OB.
(x - 2)
(x+2+3)
O c. 1-1
x
O D. 7x7 - 2x-4 + 3
Answers
Answer: B
Step-by-step explanation:
When B is simplified, it becomes x^2-3x-10. This is a polynomial because it has more than two terms(3).
Hope it helps <3
The solution is: the following is a polynomial, A. 4x^2+9x+12 & C. 15x^4
Option A and C are correct.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
Here, we have,
we know that,
A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.
A. 4x^2+9x+12 is a polynomial
B. 3-√2x is not a polynomial
C. 15x^4 is a polynomial
D. 6x^2+2/x is not a polynomial
So, Option A and C are correct.
Hence, The solution is: the following is a polynomial, A. 4x^2+9x+12 &
C. 15x^4 , Option A and C are correct.
Know more about Polynomials here:
brainly.com/question/2833285
#SPJ7
Find the angle measures given the figure is a rhombus.
Answers
Answer:
1 = 90°, 2 = 66°
Step-by-step explanation:
Since the diagonals of a rhombus are perpendicular, ∠1 = 90°. Using the Exterior Angles Theorem (exterior angle = sum of remote interior angles, we see that ∠2 = 90 - 24 = 66°.
find the value of the variable and GH if H is between G and I. GI=5b+2,HI=4b-5, HI=3
Answers
Answer:
GH = 9 units
Step-by-step explanation:
Given HI = 4b - 5 and HI 3, then
4b - 5 = 3 ( add 5 to both sides )
4b = 8 ( divide both sides by 4 )
b = 2
Thus
GI = 5b + 2 = 5(2) + 2 = 10 + 2 = 12
GH = GI - HI = 12 - 3 = 9
a car is driving at a speed of 40mi/h.what is the speed of the car in feet per minute
Answers
Answer:
[tex]\boxed{3520\ ft/min}[/tex]
Step-by-step explanation:
1 miles per hour = 88 feet per minute
Multiplying both sides by 40
40 miles per hour = 88*40 ft/min
40 mi./hr = 3520 ft/min
Answer:
3520 feet/min
Step-by-step explanation:
the speed of the car in feet per minute:
first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)
(40*5280)/1*60=3520 feet/min
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)
Answers
Answer:
(0, –2)
Step-by-step explanation:
I am assuming that point 'B' is (-5 , 0).
The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].
Apply the rule to point 'B':
[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]
B' should be (0, -2).
Answer:
Guy above me might be right but Im not sure. Im on the cumulative exam on edge.
Step-by-step explanation:
help me!!!! solve 4t+6=24
Answers
Answer:
We move all terms to the left:
4t+6-(-24)=0
We add all the numbers together, and all the variables
4t+30=0
We move all terms containing t to the left, all other terms to the right
4t=-30
t=-30/4
t=4.5
Brainiest?
Answer:
[tex]\boxed{t=\frac{9}{2} }[/tex]
Step-by-step explanation:
[tex]4t+6=24[/tex]
Subtract 6 on both sides.
[tex]4t+6-6=24-6[/tex]
[tex]4t=18[/tex]
Divide 4 on both sides.
[tex]\displaystyle \frac{4t}{4} =\frac{18}{4}[/tex]
[tex]\displaystyle t=\frac{9}{2}[/tex]
Calculate the amount of paint needed to cover the following door:
Note: You do not paint the window on the inside.
Answers
Answer:
Step-by-step explanation:
The door is shape is a combination of a rectangle and a semicircle with a square window.
Area of the door = Area of rectangle + area of a semi circle
Area of a rectangle = Length * Width (LW)
area of a semicircle = πr²/2 where r is the radius of the semi circle.
Given the length of the rectangle = 2m and its width = 1m
Area of rectangle = 2*1 = 2m²
Given the radius of the semicircle = 1/2 m
Area of the semi circle = π(0.5)²/2
= 0.25π/2
= 0.785/2
Area of the semicircle= 0.3925m²
Area of the door = 2+0.3925
Area of the door = 2.3925m²
Since we are not to paint the window, we will subtract the area of the window from the total area.
Area of the window = area of a square = 0.2*0.2
= 0.04m²
Area to be painted = Area of door - Area of the square
Area to be painted = 2.3925m² - 0.04m²
Area to be painted = 2.3535m²
Note that there was no enough information for us to calculate the amount of paint needed but knowing the area of the part to be painted can guide us.
[4 + (3 – 1)]3 = ? A. 12 B. 32 C. 64 D. 128 E. 216
Answers
Answer:
18
Step-by-step explanation:
Answer:
18.
Step-by-step explanation:
[4 + (3 - 1)] * 3
= (4 + 2) * 3
= 6 * 3
= 18
Hope this helps!
Please answer it now in two minutes
Answers
Answer:
3.9
Step-by-step explanation:
Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + 1^2 = 4^2
a^2 + 1 = 16
a^2 = 15
a = sqrt(15)
a = 3.9
Answer a = 3.9 yards
Answer:
[tex]\boxed{3.9}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
Apply Pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + 1^2 = 4^2[/tex]
[tex]a^2 + 1 = 16[/tex]
[tex]a^2 = 15[/tex]
[tex]a=\sqrt{15}[/tex]
[tex]a \approx 3.872983[/tex]
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answers
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
given that sin x equals to a over b then what is tan x
Answers
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
The coordinates of A, B, and C in the diagram are A (p, 4), B (6, 1 ), and C (9, q). Which equation correctly relates p and q? ↔ ↔ ↔ ↔ Hint: Since AB is perpendicular to BC, the slope of AB × the slope o BC = -1. A. -q − p = 7 B. q − p = 7 C. p − q = 7 D. p + q = 7
Answers
Answer:
D. p + q = 7
Step-by-step explanation:
The slope of AB is ...
mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)
The slope of BC is ...
mBC = (q -1)/(9 -6) = (q -1)/3
We want the product of these slopes to be -1:
mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)
-(q-1)/(6 -p) = -1 . . . . cancel factors of 3
q -1 = 6 -p . . . . . multiply by -(6 -p)
q + p = 7 . . . . . matches choice D
Answer:
C p+q=7
Step-by-step explanation:
I did it on plato and it was right
someone plz help !
A town currently has a population of 1,000,000, and the population is increasing 6 percent every year. Write a recursive function in now-next form to predict the population at any year in the future.
Answers
Answer:
Y=x(t)(0.06) + x
Y =predicted population
X= population currently
t= number of years
Y= 60000(t) + 1000000
Step-by-step explanation:
Let the current population be x
X= 1000000
The rate of increase= 6% each year
Let the the predicted population= y
If the population is to increase by 6% each year the function predicting the population at the future will be
Y=x(t)(0.06) + x
The only changing value in the above formula is the time.
Y= 1000000(0.06)(t) +1000000
Y= 60000(t) + 1000000
Answer: The actual answer is:
next = now x 1.06, starting at 1,000,000
PLEASE HELP! Thank you!!!
Answers
A+b is equal to 2.438 and 6.562
2.438x6.562= 15.99 which rounds up to the nearest whole number 16
16-9=7
So answer is D. 7
What is the value of y? Answer asap
Answers
Answer:
y=3
Step-by-step explanation:
10=2y+4
10-4=2y
6=2y
3=y
On a ski lift, the distance between chairs is inversely proportional to the number of chairs. At a
ski resort, one lift has 80 chairs spaced 16 meters apart. What is the constant of variation.
A.1280 B.5 C.1/5 D.1/1280
Answers
Constant of variation = number of chairs/ spacing.
80/16 = 5
The answer is B.5
Susan purchased 9/10 of a pound of shrimp for a dinner party. Her plan is to serve 1/6 of a pound of shrimp to herself and each guest. Including herself, how many people can Susan serve at her dinner party? (Remember that you can't have a fraction of a person.)
Answers
Answer:
Susan and 4 quests
5 people
Step-by-step explanation:
Take 9/10 and divide by 1/6
9/10 ÷1/6
Copy dot flip
9/10 * 6/1
54/10
50/10 + 4/10
5 4/10
We can only serve whole numbers
5 people
Susan and 4 quests
A film distribution manager calculates that 9% of the films released are flops.If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
Answers
Answer:
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
Step-by-step explanation:
Given that :
A film distribution manager calculates that 9% of the films released are flops
Let p be the probability for the movies that were released are flops;
[tex]\mu_p = P = 0.9[/tex]
If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%
now; we know that our sample size = 442
the standard deviation of the variance is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]
[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]
[tex]\sigma _p = 0.014[/tex]
So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:
[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]
[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]
[tex]P(|p-P|>0.04)=1 -0.9958[/tex]
[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]
∴
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
no clue how to do this, someone pls help
Answers
Answer:
6π
Step-by-step explanation:
First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr
Leaving it in terms of pi, the circumference is 8π
Now we need to find the length of the arc.
Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.
3/4 of 8π is 6π
The researcher is interested to know if policy A (new) is more effective than policy B (old). Frame the hypothesis and describe what each error would represent in terms of reality and conclusion.
Answers
Answer:
Null hypothesis: Policy B remains more effective than policy A.
Alternate hypothesis: Policy A is more effective than policy B.
Step-by-step explanation:
Remember, a hypothesis is a usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.
We have two types of hypothesis errors:
1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.
That is, rejecting the assumption that policy B remains more effective than policy A when it is actually true.
2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is actually false.
simplify (5 √2 - 1) ^2
Answers
What the answer please answer this question now
Answers
Answer:
[tex]m\angle Z\approx22.0\textdegree[/tex]
Step-by-step explanation:
First, note that we have a right triangle. Second, we need to find angle Z, and we are given the sides opposite to angle Z and the hypotenuse. Therefore, we can use sine.
Recall that:
[tex]\sin(\theta)=opp/hyp[/tex]
The opposite side is 3 while the hypotenuse is 8. Plug in the numbers and simplify. Use a calculator:
[tex]\sin(\angle Z)=3/8\\\angle Z=\arcsin(3/8)\\\angle Z\approx 22.0243\textdegree[/tex]
Please help I’m being timed!! A small dairy farm writes a business plan. It includes a graph showing the estimated amount of feed used each day in thousands of pounds, y, compared to the number of years since the farm began operating, x. What does the y-intercept represent? A) the estimated amount of years the farm can afford feed B) the maximum feed per day estimated for the life of the farm C) the estimated amount of feed per day for the start of the farm D) the maximum years the farm needs the originally estimated feed per day
Answers
Answer: The Answer is C
Step-by-step explanation: I just took the quiz on ed and this is the correct answer.
Answer: C: the estimated amount of feed per day for the start of the farm
Step-by-step explanation: 100% on quiz
Solve the equation for x.
Answers
Answer:
x = 27
Step-by-step explanation:
2/3x - 1/9x + 5 = 20
Subtract 5 from each side
2/3x - 1/9x + 5 -5= 20-5
2/3x - 1/9x = 15
Get a common denominator on the left side
2/3 *3/3 x - 1/9x = 15
6/9x - 1/9x = 15
5/9 x = 15
Multiply each side by 9/5
9/5 * 5/9x = 15 * 9/5
x = 15/5 *9
x = 3*9
x = 27
Answer:
x=27
Step-by-step explanation:
2/3 x -1/9 x+5=20
2/3x -1/9 x=20-5 common denominator
(6x-1x)/9=15 multiply each side by 9
(5x)=135
5x=135
x=135/5=27
x=27
Stephanie casts a shadow of 1.2 m and she is 1.8 m tall. A wind turbine casts a shadow of 10m at the same time that Stephanie measured her shadow. Draw a diagram of this situation
and then calculate how tall the wind turbine is.
Answers
Answer:
see below for a diagram15 mStep-by-step explanation:
Stephanie is 1.8/1.2 = 1.5 times as tall as her shadow is long. We expect the same is true of the wind turbine.
The wind turbine's shadow is 10 m long, so its height is 1.5·(10 m) = 15 m.
The wind turbine is 15 m tall.
The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? Consider as significant any result that differs from the mean by at least 2 standard deviations. That is, significant values are either less than or equal to muminus2sigma or greater than or equal to muplus2sigma.
Answers
Answer:
Yes, it would be statistically significant
Step-by-step explanation:
The information given are;
The percentage of jawbreakers it produces that weigh more than 0.4 ounces = 60%
Number of jawbreakers in the sample, n = 800
The mean proportion of jawbreakers that weigh more than 0.4 = 60% = 0.6 = [tex]\mu _ {\hat p}[/tex] =p
The formula for the standard deviation of a proportion is [tex]\sigma _{\hat p} =\sqrt{\dfrac{p(1-p)}{n} }[/tex]
Solving for the standard deviation gives;
[tex]\sigma _{\hat p} =\sqrt{\dfrac{0.6 \cdot (1-0.6)}{800} } = 0.0173[/tex]
Given that the mean proportion is 0.6, the expected value of jawbreakers that weigh more than 0.4 in the sample of 800 = 800*0.6 = 480
For statistical significance the difference from the mean = 2×[tex]\sigma _{\hat p}[/tex] = 2*0.0173 = 0.0346 the equivalent number of Jaw breakers = 800*0.0346 = 27.7
The z-score of 494 jawbreakers is given as follows;
[tex]Z=\dfrac{x-\mu _{\hat p} }{\sigma _{\hat p} }[/tex]
[tex]Z=\dfrac{494-480 }{0.0173 } = 230.94[/tex]
Therefore, the z-score more than 2 ×[tex]\sigma _{\hat p}[/tex] which is significant.
Answer:
Step-by-step explanation:
min 452, max 507, so 494 is not unusual.
Evaluate 7m + 2n - 8p/n for m = –4, n = 2, and p = 1.5.
Answers
Answer:
-30
Step-by-step explanation:
7m + 2n - 8p/n
Let m = –4, n = 2, and p = 1.5
7(-4) + 2 ( 2) -8*(1.5)/2
-28 + 4 - 4*1.5
-28+ 4 - 6
-30
Answer:
-30
Step-by-step explanation:
Hey there!
Well given,
m = -4
n = 2
p = 1.5
We need to plug those number into,
7m + 2n - 8p/n
7(-4) + 2(2) - 8(1.5)/(2)
-28 + 4 - 12/2
-28 + 4 - 6
-24 - 6
-30
Hope this helps :)
While watching a circus show, I counted out the number of acrobats and elephants. I counted 40 legs and 15 heads. How many acrobats did I see in the show?
Answers
Answer:
y=10 ( number of acrobat)
Step-by-step explanation:
let x be the elephant and y the acrobat
elephant has 4 legs and acrobat 2
4x+2y=40
x+y=15 ⇒x=15-y
substitute for x in the equation:
4(15-y)+2y=40
60-4y+2y=40
-2y=40-60
y=-20/-2
y=10 ( number of acrobat)
number of elephant=15-10=5 elephants
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 200 voters finds that 94 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
Answers
Answer:
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Step-by-step explanation:
From the information given :
An exit poll of 200 voters finds that 94 voted for the referendum.
How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
This implies that ;
the Sample size n = 200
the probability p = 0.52
Let X be the random variable
So; the Binomial expression can be represented as:
X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)
Mean [tex]\mu[/tex] = np
Mean [tex]\mu[/tex] = 200 × 0.52
Mean [tex]\mu[/tex] = 104
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]
The standard deviation [tex]\sigma[/tex] = 7.065
However;
P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .
The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5
Now;
x = 94.5
Therefore;
[tex]z = \dfrac{x- \mu}{\sigma}[/tex]
[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]
[tex]z = \dfrac{-9.5}{7.065}[/tex]
z = −1.345
P(X< 94.5) = P(Z < - 1.345)
From the z- table
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.